Probabilistic parameter estimation using fused data apparatus and method of use thereof

ABSTRACT

A probabilistic digital signal processor using data from multiple instruments is described. In one example, an analyzer is configured to: receive discrete first and second input data, related to a first and second sub-system of the system, from a first and second instrument, respectively. A system processor is used to fuse the first and second input data into fused data. The system processor optionally includes: (1) a probabilistic processor configured to convert the fused data into at least two probability distribution functions and (2) a dynamic state-space model, the dynamic state-space model including at least one probabilistic model configured to operate on the at least two probability distribution functions. The system processor iteratively circulates the at least two probability distribution functions in the dynamic state-space model in synchronization with receipt of updated input data, processes the probability distribution functions, and generates an output related to the state of the system.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. patent applicationSer. No. 13/181,140 filed Jul. 12, 2011, which is a continuation-in-partof U.S. patent application Ser. No. 13/181,027, filed Jul. 12, 2011,which:

is a continuation-in-part of U.S. patent application Ser. No.12/796,512, filed Jun. 8, 2010, which is a continuation-in-part of U.S.patent application Ser. No. 12/640,278, filed Dec. 17, 2009, whichclaims benefit of U.S. provisional patent application No. 61/171,802,filed Apr. 22, 2009;

claims benefit of U.S. provisional patent application No. 61/366,437filed Jul. 21, 2010;

claims benefit of U.S. provisional patent application No. 61/372,190filed Aug. 10, 2010; and

claims benefit of U.S. provisional patent application No. 61/373,809filed Aug. 14, 2010,

all of which are incorporated herein in their entirety by this referencethereto.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

The U.S. Government may have certain rights to this invention pursuantto Contract Number IIP-0839734 awarded by the National ScienceFoundation.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates generally to apparatus and methods forprocessing and/or representing sensor data, such as mechanical ormedical sensor data.

Discussion of the Related Art

Mechanical devices and biomedical monitoring devices such as pulseoximeters, glucose sensors, electrocardiograms, capnometers, fetalmonitors, electromyograms, electroencephalograms, and ultrasounds aresensitive to noise and artifacts. Typical sources of noise and artifactsinclude baseline wander, electrode-motion artifacts, physiologicalartifacts, high-frequency noise, and external interference. Someartifacts can resemble real processes, such as ectopic beats, and cannotbe removed reliably by simple filters; however, these are removable bythe techniques taught herein. In addition, mechanical devices andbiomedical monitoring devices address a limited number of parameters. Itwould be desirable to expand the number of parameters measured, such asto additional biomedical state parameters.

Patents related to the current invention are summarized herein.

Mechanical Systems

Several reports of diagnostics and prognostics applied to mechanicalsystems have been reported.

Vibrational Analysis

R. Klein “Method and System for Diagnostics and Prognostics of aMechanical System”, U.S. Pat. No. 7,027,953 B2 (Apr. 11, 2006) describesa vibrational analysis system for diagnosis of health of a mechanicalsystem by reference to vibration signature data from multiple domains,which aggregates several features applicable to a desired fault fortrend analysis of the health of the mechanical system.

Intelligent System

S. Patel, et. al. “Process and System for Developing PredictiveDiagnostic Algorithms in a Machine”, U.S. Pat. No. 6,405,108 B1 (Jun.11, 2002) describe a process for developing an algorithm for predictingfailures in a system, such as a locomotive, comprising conducting afailure mode analysis to identify a subsystem, collecting expert data onthe subsystem, and generating a predicting signal for identifyingfailure modes, where the system uses external variables that affect thepredictive accuracy of the system.

C. Bjornson, “Apparatus and Method for Monitoring and Maintaining PlantEquipment”, U.S. Pat. No. 6,505,145 B1 (Jan. 11, 2003) describes acomputer system that implements a process for gathering, synthesizing,and analyzing data related to a pump and/or a seal, in which data aregathered, the data is synthesized and analyzed, a root cause isdetermined, and the system suggests a corrective action.

C. Bjornson, “Apparatus and Method for Monitoring and Maintaining PlantEquipment”, U.S. Pat. No. 6,728,660 B2 (Apr. 27, 2004) describes acomputer system that implements a process for gathering, synthesizing,and analyzing data related to a pump and/or a seal, in which data aregathered, the data is synthesized and analyzed, and a root cause isdetermined to allow a non-specialist to properly identify and diagnose afailure associated with a mechanical seal and pump.

K. Pattipatti, et. al. “Intelligent Model-Based Diagnostics for SystemMonitoring, Diagnosis and Maintenance”, U.S. Pat. No. 7,536,277 B2 (May19, 2009) and K. Pattipatti, et. al. “Intelligent Model-BasedDiagnostics for System Monitoring, Diagnosis and Maintenance”, U.S. Pat.No. 7,260,501 B2 (Aug. 21, 2007) both describe systems and methods formonitoring, diagnosing, and for condition-based maintenance of amechanical system, where model-based diagnostic methodologies combine orintegrate analytical models and graph-based dependency models to enhancediagnostic performance.

Inferred Data

R. Tryon, et. al. “Method and Apparatus for Predicting Failure in aSystem”, U.S. Pat. No. 7,006,947 B2 (Feb. 28, 2006) describe a methodand apparatus for predicting system failure or reliability using acomputer implemented model relying on probabilistic analysis, where themodel uses data obtained from references and data inferred from acquireddata. More specifically, the method and apparatus uses a pre-selectedprobabilistic model operating on a specific load to the system while thesystem is under operation.

Virtual Prototypinq

R. Tryon, et. al. “Method and Apparatus for Predicting Failure of aComponent”, U.S. Pat. No. 7,016,825 B1 (Mar. 21, 2006) describe a methodand apparatus for predicting component failure using a probabilisticmodel of a material's microstructural-based response to fatigue usingvirtual prototyping, where the virtual prototyping simulates grain size,grain orientation, and micro-applied stress in fatigue of the component.

R. Tryon, et. al. “Method and Apparatus for Predicting Failure of aComponent, and for Determining a Grain Orientation Factor for aMaterial”, U.S. Pat. No. 7,480,601 B2 (Jan. 20, 2009) describe a methodand apparatus for predicting component failure using a probabilisticmodel of a material's microstructural-based response to fatigue using acomputer simulation of multiple incarnations of real material behavioror virtual prototyping.

Medical Systems

Several reports of systems applied to biomedical systems have beenreported.

Lung Volume

M. Sackner, et. al. “Systems and Methods for Respiratory EventDetection”, U.S. patent application no. 2008/0082018 A1 (Apr. 3, 2008)describe a system and method of processing respiratory signals frominductive plethysmographic sensors in an ambulatory setting that filtersfor artifact rejection to improve calibration of sensor data and toproduce output indicative of lung volume.

Pulse Oximeter

J. Scharf, et. al. “Separating Motion from Cardiac Signals Using SecondOrder Derivative of the Photo-Plethysmograph and Fast FourierTransforms”, U.S. Pat. No. 7,020,507 B2 (Mar. 28, 2006) describes theuse of filtering photo-plethysmograph data in the time domain to removemotion artifacts.

M. Diab, et. al. “Plethysmograph Pulse Recognition Processor”, U.S. Pat.No. 6,463,311 B1 (Oct. 8, 2002) describe an intelligent, rule-basedprocessor for recognition of individual pulses in a pulseoximeter-derived photo-plethysmograph waveform operating using a firstphase to detect candidate pulses and a second phase applying aplethysmograph model to the candidate pulses resulting in period andsignal strength of each pulse along with pulse density.

C. Baker, et. al. “Method and Apparatus for Estimating PhysiologicalParameters Using Model-Based Adaptive Filtering”, U.S. Pat. No.5,853,364 (Dec. 29, 1998) describe a method and apparatus for processingpulse oximeter data taking into account physical limitations usingmathematical models to estimate physiological parameters.

Cardiac

J. McNames, et. al. “Method, System, and Apparatus for CardiovascularSignal Analysis, Modeling, and Monitoring”, U.S. patent applicationpublication no. 2009/0069647 A1 (Mar. 12, 2009) describe a method andapparatus to monitor arterial blood pressure, pulse oximetry, andintracranial pressure to yield heart rate, respiratory rate, and pulsepressure variation using a statistical state-space model ofcardiovascular signals and a generalized Kalman filter to simultaneouslyestimate and track the cardiovascular parameters of interest.

M. Sackner, et. al. “Method and System for Extracting Cardiac Parametersfrom Plethysmograph Signals”, U.S. patent application publication no.2008/0027341 A1 (Jan. 31, 2008) describe a method and system forextracting cardiac parameters from ambulatory plethysmographic signal todetermine ventricular wall motion.

Hemorrhage

P. Cox, et. al. “Methods and Systems for Non-Invasive InternalHemorrhage Detection”, International Publication no. WO 2008/055173 A2(May 8, 2008) describe a method and system for detecting internalhemorrhaging using a probabilistic network operating on data from anelectrocardiogram, a photoplethysmogram, and oxygen, respiratory, skintemperature, and blood pressure measurements to determine if the personhas internal hemorrhaging.

Disease Detection

V. Karlov, et. al. “Diagnosing Inapparent Diseases From Common ClinicalTests Using Bayesian Analysis”, U.S. patent application publication no.2009/0024332 A1 (Jan. 22, 2009) describe a system and method ofdiagnosing or screening for diseases using a Bayesian probabilityestimation technique on a database of clinical data.

Statement of the Problem

Mechanical and biomedical sensors are typically influenced by multiplesources of contaminating signals that often overlap the frequency of thesignal of interest, making it difficult, if not impossible, to applyconventional filtering. Severe artifacts such as occasional signaldropouts due to sensor movement or large periodic artifacts are alsodifficult to filter in real time. Biological sensor hardware can beequipped with a computer comprising software for post-processing dataand reducing or rejecting noise and artifacts. Current filteringtechniques typically use some knowledge of the expected frequencies ofinterest where the sought-after physiological information should befound.

Adaptive filtering has been used to attenuate artifacts in pulseoximeter signals corrupted with overlapping frequency noise bands byestimating the magnitude of noise caused by patient motion and otherartifacts and canceling its contribution from pulse oximeter signalsduring patient movement. Such a time correlation method relies on aseries of assumptions and approximations to the expected signal, noise,and artifact spectra, which compromises accuracy, reliability, andgeneral applicability.

Filtering techniques based on Kalman and extended Kalman techniquesoffer advantages over conventional methods and work well for filteringlinear systems or systems with small nonlinearities and Gaussian noise.These filters, however, are not adequate for filtering highly nonlinearsystems and non-Gaussian/non-stationary noise. Therefore, obtainingreliable biomedical signals continue to present problems, particularlywhen measurements are made in mobile, ambulatory, and physically activepatients.

Existing data processing techniques, including adaptive noisecancellation filters, are unable to extract information that is hiddenor embedded in biomedical signals and also discard some potentiallyvaluable information.

Existing medical sensors sense a narrow spectrum of medical parametersand states. What is needed is a system readily expanding the number ofbiomedical states determined.

A method or apparatus for extracting additional useful information froma mechanical sensor in a mechanical system, a biomedical system, and/ora system component or sub-component is needed to provide usersadditional and/or clearer information.

SUMMARY OF THE INVENTION

The invention comprises use of fused data in a probabilistic model toextract, filter, estimate and/or add additional information about asystem based on data from a sensor.

DESCRIPTION OF THE FIGURES

A more complete understanding of the present invention is derived byreferring to the detailed description and claims when considered inconnection with the Figures, wherein like reference numbers refer tosimilar items throughout the Figures.

FIG. 1 illustrates operation of the intelligent data extractionalgorithm on a biomedical apparatus;

FIG. 2 provides a block diagram of a data processor;

FIG. 3 is a flow diagram of a probabilistic digital signal processor;

FIG. 4 illustrates a dual estimator;

FIG. 5 expands the dual estimator;

FIG. 6 illustrates state and model parameter estimators;

FIG. 7 provides inputs and internal operation of a dynamic state-spacemodel;

FIG. 8 is a flow chart showing the components of a hemodynamics dynamicstate-space model;

FIG. 9A illustrates input sensor data; FIG. 9B illustrates processedoutput data of heart rate; FIG. 9C illustrates stroke volume; FIG. 9Dillustrates cardiac output; FIG. 9E illustrates oxygen percentage; andFIG. 9F illustrates aortic and radial pressure from a data processorconfigured to process pulse oximetry data;

FIG. 10A illustrates input sensor data and processed output data; FIGS.10(B-E) illustrate processed data from a data processor configured toprocess pulse oximetry data under a low blood perfusion condition;

FIG. 11 is a flow chart showing the components of a electrocardiographdynamic state-space model;

FIG. 12A illustrates noisy non-stationary ECG sensor data input andprocessed ECG output and FIG. 12B illustrates noisy and processed heartrate sensor data;

FIG. 13A and FIG. 13B illustrate input ECG sensor data and compareoutput data from a data processor according to the present inventionwith output data generating using a Savitzky-Golay FIR data processingalgorithm;

FIG. 14 illustrates fusion of data from multiple instruments;

FIG. 15 illustrates fusion of biomedical data, accelerometer data,and/or environmental data;

FIG. 16 shows integration of multiple data streams into a jointprocessor;

FIG. 17 illustrates a fusion dynamic state-space model;

FIG. 18 illustrates combination of medical data streams into a physicsbased model; and

FIG. 19 provides a flowchart of dynamic state-space model diagnosticsused as prognosis and control.

DETAILED DESCRIPTION OF THE INVENTION

The invention comprises use of a method, a system, and/or an apparatususing a probabilistic model for monitoring and/or estimating a parameterusing fused data from multiple sensors.

The system applies to the mechanical and medical fields. Herein, forclarity the system is applied to biomedical devices, though the systemconcepts apply to mechanical apparatus.

In one embodiment, an intelligent data extraction algorithm (IDEA) isused in a system, which combines a dynamic state-space model with aprobabilistic digital signal processor to estimate a parameter, such asa biomedical parameter. Initial probability distribution functions areinput to a dynamic state-space model, which iteratively operates onprobability distribution functions (PDFs), such as state and modelprobability distribution functions, to generate a prior probabilitydistribution function, which is input into a probabilistic updater. Theprobabilistic updater integrates sensor data with the prior probabilitydistribution function to generate a posterior probability distributionfunction passed to a probabilistic sampler, which estimates one or moreparameters using the posterior, which is output or re-sampled and usedas an input to the dynamic state-space model in the iterative algorithm.In various embodiments, the probabilistic data signal processor is usedto filter output and/or estimate a value of a new physiologicalparameter from a biomedical device using appropriate physical models,which optionally include biomedical, chemical, electrical, optical,mechanical, and/or fluid based models. For clarity, examples of heartand cardiovascular medical devices are provided.

In one example, an analyzer is configured to: (1) receive discrete firstinput data, related to a first sub-system of the system, from a firstinstrument and (2) receive discrete second input data, related to asecond sub-system of the system, from a second instrument. The analyzeroptionally includes a system processor configured to fuse the firstinput data and the second input data into fused data. The systemprocessor optionally includes: (1) a probabilistic processor configuredto convert the fused data into at least two probability distributionfunctions and (2) a dynamic state-space model, the dynamic state-spacemodel including at least one probabilistic model configured to operateon the at least two probability distribution functions. The systemprocessor iteratively circulates the at least two probabilitydistribution functions in the dynamic state-space model insynchronization with receipt of at least one of: (1) updated first inputdata and (2) updated second input data. The system processor is furtherconfigured to process the probability distribution functions to generatean output related to the state of the system.

In another example, an analyzer is configured for processing sensor datarepresentative of a body where the analyzer includes: a physical modelrepresentative of function of a body constituent; the physical modelcoded into a digital signal processor electrically connected to acomputer embedded in the analyzer. The digital signal processor isconfigured to: (1) generate a prior probability distribution functionusing the physical model and (2) repetitively fuse input dataoriginating from at least two types of medical instruments with theprior probability distribution function to generate a posteriorprobability distribution function. Further, the processor is configuredto process the posterior probability distribution function to generatean output of at least one of: (1) a monitored parameter valuerepresentative of the body and (2) an estimated parameter valuerepresentative of the body.

In various embodiments, the probabilistic digital signal processorcomprises one or more of a dynamic state-space model, a dual or jointupdater, and/or a probabilistic sampler, which process input data, suchas sensor data and generates an output. Preferably, the probabilisticdigital signal processor (1) iteratively processes the data and/or (2)uses a mathematical model of the physical system in processing the inputdata.

The probabilistic digital signal processor optionally:

-   -   operates on or in conjunction with a sensor in a mechanical        system;    -   filters input data;    -   operates using data from a medical meter, where the medical        meter yields a first physical parameter from raw data, to        generate a second physical parameter not output by the medical        meter;    -   operates on discrete/non-probabilistic input data, such as from        a mechanical device or a medical device to generate a        probabilistic output function;    -   iteratively circulates or dynamically circulates a probability        distribution function through at least two of the dynamic        state-space model, the dual or joint updater, and/or the        probabilistic sampler;    -   fuses or combines output from multiple sensors, such as two or        more medical devices; and    -   prognosticates probability of future events.

To facilitate description of the probabilistic digital signal processor,a non-limiting example of a hemodynamics process model is provided. Inthis example, the probabilistic digital signal processor is provided:

-   -   raw sensor data, such as current, voltage, and/or resistance;        and/or    -   output from a medical device to a first physical or chemical        parameter.

In this example, the medical device is a pulse oximeter and the firstparameter from the pulse oximeter provided as input to the probabilisticdigital signal processor is one or more of:

-   -   raw data, such as a voltage waveform that correlates to light        absorption by blood;    -   heart rate; and/or    -   blood oxygen saturation.

The probabilistic digital signal processor uses a physical model, suchas a probabilistic model, to operate on the first physical parameter togenerate a second physical parameter, where the second physicalparameter is not the first physical parameter. For example, the outputof the probabilistic digital signal processor when provided with thepulse oximeter data is one or more of:

-   -   a heart stroke volume;    -   a cardiac output flow rate;    -   an aortic blood pressure; and/or    -   a radial blood pressure.

Optionally, the output from the probabilistic model is an updated, anerror filtered, and/or a smoothed version of the original input data,such as a smoothed blood oxygen saturation percentage as a function oftime. The hemodynamics model is further described, infra.

To facilitate description of the probabilistic digital signal processor,another non-limiting example of an electrocardiograph process model isprovided. In this example, the probabilistic digital signal processor isprovided:

-   -   raw sensor data, such as intensity, an electrical current,        and/or a voltage; and/or    -   output from a medical device, such as an electrocardiogram, to a        first physical or electrical parameter.

In this example, the medical device is a electrocardiograph and thefirst physical or electrical parameter from the electrocardiographsystem provided as input to the probabilistic digital signal processoris one or more of:

-   -   raw data; and/or    -   an electrocardiogram.

The probabilistic digital signal processor uses a physical model, suchas a probabilistic model, to operate on the first physical parameter togenerate a second physical parameter or an indicator, where the secondphysical parameter is not the first physical parameter. For example, theoutput of the probabilistic digital signal processor when provided withthe electrocardiogram or raw data is one or more of:

-   -   an arrhythmia detection;    -   an ischemia warning; and/or    -   a heart attack prediction.

Optionally, the output from the probabilistic model is an updated, errorfiltered, or smoothed version of the original input data. For example,the probabilistic processor uses a physical model where the output ofthe model processes low signal-to-noise ratio events to yield an earlywarning of any of the arrhythmia detection, the ischemia warning, and/orthe heart attack prediction. The electrocardiograph model is furtherdescribed, infra.

To still further facilitate description of the probabilistic digitalsignal processor, non-limiting fusion examples are provided, whichcombine data from one or more of:

-   -   a mechanical system;    -   a sensor monitoring a mechanical device;    -   an electrodynamics based medical device;    -   a hemodynamic based medical device;    -   accelerometer data; and    -   an environmental meter.

As further described, supra, fusion of signals or sensor data from aplurality of devices allows:

-   -   detection of a false positive or false negative signal from a        first device with a second device;    -   noise recognized in first sensor data as the noise is not        present in a second sensor type or is correlated with noise of        the second sensor type;    -   fusion of environmental data with medical data;    -   determination of an additional parameter not independently        measured with individual data types of the fused data;    -   electrocardiograph data to aid in analysis of pulse oximeter        data and vise-versa; and/or    -   electrodynamic information to aid in analysis of hemodynamic        information and vise-versa.

Deterministic Vs. Probabilistic Models

Typically, computer-based systems use a mapping between observedsymptoms of failure and the equipment where the mapping is built usingdeterministic techniques. The mapping typically takes the form of alook-up table, a symptom-problem matrix, trend analysis, and productionrules. In stark contrast, alternatively probabilistic models are used toanalyze a system. An example of a probabilistic model, referred toherein as an intelligent data extraction system is provided, infra.

Intelligent Data Extraction System

Referring now to FIG. 1, an algorithm based intelligent data extractionsystem 100 is illustrated. The intelligent data extraction system 100uses a controller 110 to control a sensor 120. The sensor 120 is used tomeasure a parameter and/or is incorporated into a biomedical apparatus130. Optionally, the controller 110 additionally controls the medicalapparatus and/or is built into the biomedical apparatus 130. The sensor120 provides readings to a data processor or a probabilistic digitalsignal processor 200, which provides feedback to the controller 110and/or provides output 150. In one embodiment, the controller 110comprises a microprocessor in a computer or computer system, an embeddeddevice, and/or an embedded processor.

Herein, to enhance understanding and for clarity of presentation,non-limiting examples of an intelligent data extraction system operatingon a hemodynamics biomedical devices are used to illustrate methods,systems, and apparatus described herein. Generally, the methods,systems, and apparatus described herein extend to any apparatus having amoveable part and/or to any medical device. Examples of the dynamicstate-space model with a probabilistic digital signal processor used toestimate parameters of additional biomedical systems are provided afterthe details of the processing engine are presented.

Still referring to FIG. 1, in a pulse oximeter example the controller110 controls a sensor 120 in the pulse oximeter apparatus 130. Thesensor 120 provides readings, such as a spectral reading to theprobabilistic digital signal processor 200, which is preferably aprobability based data processor. The probabilistic digital signalprocessor 200 optionally operates on the input data or provides feedbackto the controller 110, such as state of the patient, as part of a loop,iterative loop, time series analysis, and/or generates the output 150,such as a smoothed biomedical state parameter or a new biomedical stateparameter. For clarity, the pulse oximeter apparatus is usedrepetitively herein as an example of the biomedical apparatus 130 uponwhich the intelligent data extraction system 100 operates. Theprobabilistic digital signal processor 200 is further described, infra.

Data Processor

Referring now to FIG. 2, the probabilistic digital signal processor 200of the intelligent data extraction system 100 is further described.Generally, the data processor includes a dynamic state-space model 210(DSSM) and a probabilistic updater 220 that iteratively or sequentiallyoperates on sensor data 122 from the sensor 120. The probabilisticupdater 220 outputs a probability distribution function to a parameterupdater or a probabilistic sampler 230, which generates one or moreparameters, such as an estimated diagnostic parameter, which is sent tothe controller 110, is used as part of an iterative loop as input to thedynamic state-space model 210, and/or is a basis of the output 150. Thedynamic state-space model 210 and probabilistic updater 220 are furtherdescribed, infra.

Referring now to FIG. 3, the probabilistic digital signal processor 200is further described. Generally, a probability function, a probabilitydistribution function (PDF), an initial probability distributionfunction, or a set of initial probability distribution functions 310 areinput to the dynamic state-space model 210. In a process 212, thedynamic state-space model 210 operates on the initial probabilitydistribution functions 310 to generate a prior probability distributionfunction, hereinafter also referred to as a prior or as a prior PDF. Forexample, an initial state parameter 312 probability distributionfunction and an initial model parameter 314 probability distributionfunction are provided as initial inputs to the dynamic state-space model210. The dynamic state-space model 210 operates on the initial stateparameter 312 and/or initial model parameter 314 to generate the priorprobability distribution function, which is input to the probabilisticupdater 220. In a process 320, the probabilistic updater 220 integratessensor data, such as timed sensor data 122, by operating on the sensordata and on the prior probability distribution function to generate aposterior probability distribution function, herein also referred to asa posterior or as a posterior PDF. In a process 232, the probabilisticsampler 230 estimates one or more parameters using the posteriorprobability distribution function. The probabilistic sampler 230operates on the state and model parameter probability distributionfunctions from the state and model parameter updaters 224, 226,respectively or alternatively operates on the joint parameterprobability distribution function and calculates an output. The outputis optionally:

-   -   the state or joint parameter PDF, passed to the PDF resampler        520; and/or;    -   output values resulting from an operation on the inputs to the        output 150 or output display or to the 110 controller.

In one example, expectation values such as a mean and a standarddeviation of a state parameter are calculated from the state parameterPDF and output to the user, such as for diagnosis. In another example,expectation values, such as a mean value of state and model parameters,are calculated and then used in a model to output a more advanceddiagnostic or prognostic parameter. In a third example, expectationvalues are calculated on a PDF that is the result of an operation on thestate parameter PDF and/or model parameter PDF. Optionally, the outputis to the same parameter as the state parameter PDF or model parameterPDF. Other data, such as user-input data, is optionally used in theoutput operation. The estimated parameters of the probabilistic sampler230 are optionally used as a feedback to the dynamic state-space model210 or are used to estimate a biomedical parameter. The feedback to thedynamic state-space model 210 is also referred to as a new probabilitydistribution function or as a new PDF, which is/are updates of theinitial state parameter 312 and/or are updates of the initial modelparameter 314. Again, for clarity, an example of an estimated parameter232 is a measurement of the heart/cardiovascular system, such as aheartbeat stroke volume.

Dual Estimator

In another embodiment, the probabilistic updater 220 of theprobabilistic digital signal processor 200 uses a dual or jointestimator 222. Referring now to FIG. 4, the joint estimator 222 or dualestimation process uses both a state parameter updater 224 and a modelparameter updater 226. Herein, for clarity, a dual estimator 222 isdescribed. However, the techniques and steps described herein for thedual estimator are additionally applicable to a joint estimator as thestate parameter and model parameter vector and/or matrix of the dualestimator are merely concatenated in a joint parameter vector and/or arejoined in a matrix in a joint estimator.

State Parameter Updater

A first computational model used in the probabilistic updater 220includes one or more state variables or state parameters, whichcorrespond to the parameter being estimated by the state parameterupdater 224. In the case of the hemodynamics monitoring apparatus, stateparameters include time, intensity, reflectance, and/or a pressure. Someor all state parameters are optionally selected such that they representthe “true” value of noisy timed sensor data. In this case, calculationof such a posterior state parameter PDF constitutes a noise filteringprocess and expectation values of the PDF optionally represent filteredsensor values and associated confidence intervals.

Model Parameter Updater

A second computational model used in the probabilistic updater 220includes one or more model parameters updated in the model parameterupdater 226. For example, in the case of the hemodynamics monitoringapparatus, model parameters include: a time interval, a heart rate, astroke volume, and/or a blood oxygenation percentage.

Hence, the dual estimator 222 optionally simultaneously or in aprocessing loop updates or calculates one or both of the stateparameters and model parameters. The probabilistic sampler 230 is usedto determine the estimated value for the biomedical parameter, which isoptionally calculated from a state parameter, a model parameter, or acombination of one or more of the state parameter and/or the modelparameter.

Referring still to FIGS. 3 and 4 and now referring to FIG. 5, a firstexample of the dual estimator 222 is described and placed into contextof the dynamic state-space model 210 and probabilistic sampler 230 ofthe probabilistic digital signal processor 200. The state parameterupdater 224 element of the dual estimator 222 optionally:

-   -   uses a sensor data integrator 320 operating on the prior PDF        being passed from the dynamic state-space model 210 and        optionally operates on new timed sensor data 122, to produce the        posterior PDF passed to the probabilistic sampler 230;    -   operates on current model parameters 510; and/or    -   in a process 520, the state parameter updater 224 optionally        re-samples a probability distribution function passed from the        probabilistic sampler 230 to form the new probability        distribution function passed to the dynamic state-space model        210.

In addition, in a process 530 the model parameter updater 226 optionallyintegrates new timed sensor data 122 with output from the probabilisticsampler 230 to form new input to the dynamic state-space model 210.

Referring now to FIG. 6, a second example of a dual estimator 222 isdescribed. In this example:

-   -   initial state parameter probability distribution functions 312        are passed to the dynamic state-space model 210; and/or    -   initial model parameter probability distribution functions 314        are passed to the dynamic state-space model 210.

Further, in this example:

-   -   a Bayesian rule applicator 322 is used as an algorithm in the        sensor data integrator 320;    -   a posterior distribution sample algorithm 522 is used as the        algorithm in the resampling of the PDF process 520; and    -   a supervised or unsupervised machine learning algorithm 532 is        used as the algorithm in the model parameter updater 530.

Filtering

In various embodiments, algorithms, data handling steps, and/ornumerical recipes are used in a number of the steps and/or processesherein. The inventor has determined that several algorithms areparticularly useful: sigma point Kalman filtering, sequential MonteCarlo filtering, and/or use of a sampler. In a first example, either thesigma point Kalman filtering or sequential Monte Carlo algorithms areused in generating the probability distribution function. In a secondexample, either the sigma point Kalman filtering or sequential MonteCarlo algorithms are used in the unsupervised machine learning 532 stepin the model parameter updater 530 to form an updated model parameter.The sigma point Kalman filtering, sequential Monte Carlo algorithms, anduse of a sampler are further described, infra.

Sigma Point Kalman Filter

Filtering techniques based on Kalman and extended Kalman techniquesoffer advantages over conventional methods and work well for filteringlinear systems or systems with small nonlinearities and Gaussian noise.These Kalman filters, however, are not optimum for filtering highlynonlinear systems and/or non-Gaussian/non-stationary noise. In starkcontrast, sigma point Kalman filters are well suited to data havingnonlinearities and non-Gaussian noise.

Herein, a sigma point Kalman filter (SPKF) refers to a filter using aset of weighted sigma-points that are deterministically calculated, suchas by using the mean and square-root decomposition, or an equivalent, ofthe covariance matrix of a probability distribution function to aboutcapture or completely capture at least the first and second ordermoments. The sigma-points are subsequently propagated in time throughthe dynamic state-space model 210 to generate a prior sigma-point set.Then, prior statistics are calculated using tractable functions of thepropagated sigma-points, weights, and new measurements.

Sigma point Kalman filter advantages and disadvantages are describedherein. A sigma point Kalman filter interprets a noisy measurement inthe context of a mathematical model describing the system andmeasurement dynamics. This gives the sigma point Kalman filter inherentsuperior performance to all “model-less” methods, such as Wienerfiltering, wavelet de-noising, principal component analysis, independentcomponent analysis, nonlinear projective filtering, clustering methods,adaptive noise cancelling, and many others.

A sigma point Kalman filter is superior to the basic Kalman filter,extended Kalman filter, and related variants of the Kalman filters. Theextended Kalman filter propagates the random variable using a singlemeasure, usually the mean, and a first order Taylor expansion of thenonlinear dynamic state-space model 210. Conversely, a sigma pointKalman filter decomposes the random variable into distribution momentsand propagates those using the unmodified nonlinear dynamic state-spacemodel 210. As a result, the sigma point Kalman filter yields higheraccuracy with equal algorithm complexity, while also being easier toimplement in practice.

In the sigma-point formalism the probability distribution function isrepresented by a set of values called sigma points, those valuesrepresent the mean and other moments of the distribution which, wheninput into a given function, recovers the probability distributionfunction.

Sequential Monte Carlo

Sequential Monte Carlo (SMC) methods approximate the prior probabilitydistribution function through use of a set of weighted sample valueswithout making assumptions about its form. The samples are thenpropagated in time through the unmodified dynamic state-space model 210.The resulting samples are used to update the posterior via Bayes ruleand the latest noisy measurement or timed sensor data 122.

In the sequential Monte Carlo formalism the PDF is actually discretizedinto a collection of probability “particles” each representing a segmentof the probability density in the probability distribution function.

SPKF and SMC

In general, sequential Monte Carlo methods have analysis advantagescompared to the sigma point Kalman filters, but are more computationallyexpensive. However, the SPKF uses a sigma-point set, which is an exactrepresentation only for Gaussian probability distribution functions(PDFs). As a result, SPKFs lose accuracy when PDFs depart heavily fromthe Gaussian form, such as with bimodal, heavily-tailed, ornonstationary distributions. Hence, both the SMC and SPKF filters haveadvantages. However, either a SMC analysis or SPKF is used to propagatethe prior using the unmodified DSSM. Herein, generally when a SMC filteris used a SPKF filter is optionally used and vise-versa.

A SPKF or a SMC algorithm is used to generate a reference signal in theform of a first probability distribution from the model's current(time=t) physiological state. The reference signal probabilitydistribution and a probability distribution generated from a measuredsignal from a sensor at a subsequent time (time=t+n) are convolutedusing Bayesian statistics to estimate the true value of the measuredphysiological parameter at time=t+n. The probability distributionfunction is optionally discrete or continuous. The probabilitydistribution function is optionally used to identify the probability ofeach value of an unidentified random variable, such as in a discretefunction, or the probability of the value falling within a particularinterval, such as in a continuous function.

Sampler

Probability distribution functions (PDFs) are optionally continuous ordiscrete. In the continuous case the probability distribution functionis represented by a function. In the discrete case, the variable spaceis binned into a series of discrete values. In both the continuous anddiscrete cases, probability distribution functions are generated byfirst decomposing the PDF into a set of samplers that are characteristicof the probability distribution function and then the samplers arepropagated via computations through the DSSM (prior generation) andsensor data integrator (posterior generation). Herein, a sampler is acombination of a value and label. The value is associated with thex-axis of the probability distribution function, which denotes state,model, or joint parameters. The label is associated with the y-axis ofthe probability distribution function, which denotes the probability.Examples of labels are: weight, frequency, or any arbitrary moment of agiven distribution, such as a first Gaussian moment. A powerful exampleof characteristic sampler use is decomposing the PDF into a series ofstate values with attached first Gaussian moment labels. This sum ofseveral Gaussian distributions with different values and moments usuallygives accurate approximations of the true probability distributionfunction.

Probabilistic Digital Signal Processor

As described, supra, in various embodiments, the probabilistic digitalsignal processor 200 comprises one or more of a dynamic state-spacemodel 210, a dual or joint estimator 222, and/or a probabilistic sampler230, which processes input data, such as sensor data 122 and generatesan output 150. Preferably, the probabilistic digital signal processor200 (1) iteratively processes the data and/or (2) uses a physical modelin processing the input data.

The probabilistic digital signal processor 200 optionally:

-   -   filters input data;    -   operates using data from a medical meter, where the medical        meter yields a first physical parameter from raw data, to        generate a second physical parameter not output by the medical        meter;    -   operates on discrete/non-probabilistic input data from a medical        device to generate a probabilistic output function;    -   iteratively circulates a probability distribution function        through at least two of the dynamic state-space model, the dual        or joint updater, and/or the probabilistic sampler;    -   fuses or combines output from multiple medical devices; and/or    -   prognosticates probability of future events.

A hemodynamics example of a probabilistic digital signal processor 200operating on data from a pulse oximeter is used to describe theseprocesses, infra.

Dynamic State-Space Model

The dynamic state-space model 210 is further described herein.

Referring now to FIG. 7, schematics of an exemplary dynamic state-spacemodel 210 (DSSM) used in the processing of data is provided. The dynamicstate-space model 210 typically and optionally includes a process model710 and/or an observation model 720. The process model 710, F, whichmathematically represents mechanical processes involved in generatingone or more biomedical parameters, is measured by a sensor, such as asensor sensing a mechanical component and describes the state of thebiomedical apparatus, output of the biomedical apparatus, and/or stateof the patient over time in terms of state parameters. This mathematicalmodel optimally includes mathematical representations accounting forprocess noise 750, such as mechanically caused artifacts that may causethe sensor to produce a digital output that does not produce an accuratemeasurement for the biomedical parameter being sensed. The dynamicstate-space model 210 also comprises an observational model 720, H,which mathematically represents processes involved in collecting sensordata measured by the mechanical sensor. This mathematical modeloptimally includes mathematical representations accounting forobservation noise produced by the sensor apparatus that may cause thesensor to produce a digital output that does not produce an accuratemeasurement for a biomedical parameter being sensed. Noise terms in themathematical models are not required to be additive.

While the process and observation mathematical models 710, 720 areoptionally conceptualized as separate models, they are preferablyintegrated into a single mathematical model that describes processesthat produce a biomedical parameter and processes involved in sensingthe biomedical parameter. The integrated process and observation model,in turn, is integrated with a processing engine within an executableprogram stored in a data processor, which is configured to receivedigital data from one or more sensors and to output data to a displayand/or to another output format.

Still referring to FIG. 7, inputs into the dynamic state-space model 210include one or more of:

-   -   state parameters 730, such as the initial state parameter        probability distribution function 312 or the new PDF;    -   model parameters 740, such as the initial noise parameter        probability distribution function 314 or an updated model        parameter from the unsupervised machine learning module 532;    -   process noise 750; and/or    -   observation noise 760.

Hemodynamics Dynamic State-Space Model

A first non-limiting specific example is used to facilitateunderstanding of the dynamic state-space model 210. Referring now toFIG. 8, a hemodynamics dynamic state-space model 805 flow diagram ispresented. Generally, the hemodynamics dynamic state-space model 805 isan example of a dynamic state-space model 210. The hemodynamics dynamicstate-space model 805 combines sensor data 122, such as a spectralreadings of skin, with a physical parameter based probabilistic model.The hemodynamics dynamic state-space model 805 operates in conjunctionwith the probabilistic updater 220 to form an estimate ofheart/cardiovascular state parameters.

To facilitate description of the probabilistic digital signal processor,a non-limiting example of a hemodynamics process model is provided. Inthis example, the probabilistic digital signal processor is provided:

-   -   raw sensor data, such as current, voltage, and/or resistance;        and/or    -   a first physical parameter output from a medical device.

In this example, the medical device is a pulse oximeter collecting rawdata and the first physical parameter from the pulse oximeter providedas input to the probabilistic digital signal processor is one or moreof:

-   -   a heart rate; and/or    -   a blood oxygen saturation.

The probabilistic digital signal processor uses a physical model, suchas a probabilistic model, to operate on the first physical parameterand/or the raw data to generate a second physical parameter, where thesecond physical parameter is optionally not the first physicalparameter. For example, the output of the probabilistic digital signalprocessor using a physical hemodynamic model, when provided with thepulse oximeter data, is one or more of:

-   -   a heart stroke volume;    -   a cardiac output flow rate;    -   an aortic blood pressure; and/or    -   a radial blood pressure.

Optionally, the output from the probabilistic model is an updated, errorfiltered, and/or smoothed version of the original input data, such as asmoothed blood oxygen saturation percentage as a function of time.

Still referring to FIG. 8, to facilitate description of the hemodynamicsdynamic state-space model 805, a non-limiting example is provided. Inthis example, the hemodynamics dynamic state-space model 805 is furtherdescribed. The hemodynamics dynamic state-space model 805 preferablyincludes a hemodynamics process model 810 corresponding to the dynamicstate-space model 210 process model 710. Further, the hemodynamicsdynamic state-space model 805 preferably includes a hemodynamicsobservation model 820 corresponding to the dynamic state-space model 210observation model 720. The hemodynamics process model 810 andhemodynamics observation model 820 are further described, infra.

Still referring to FIG. 8, the hemodynamics process model 810 optionallyincludes one or more of a heart model 812, a vascular model 814, and/ora light scattering or light absorbance model 816. The heart model 812 isa physics based probabilistic model of the heart and movement of bloodin and/or from the heart. The vascular model 814 is a physics basedprobabilistic model of movement of blood in arteries, veins, and/orcapillaries. The various models optionally share information. Forexample, blood flow or stroke volume exiting the heart in the heartmodel 812 is optionally an input to the arterial blood in the vascularmodel 814. The light scattering and/or absorbance model 816 relatesspectral information, such as from a pulse oximeter, to additionalhemodynamics dynamic state-space model parameters, such as heart rate(HR), stroke volume (SV), and/or whole-blood oxygen saturation (SpO₂) oroxyhemoglobin percentage.

Still referring to FIG. 8, the hemodynamics observation model 820optionally includes one or more of a sensor dynamics and noise model 822and/or a spectrometer signal transduction noise model 824. Each of thesensor dynamics and noise model 822 and the spectrometer signaltransduction noise model 824 are physics based probabilistic modelsrelated to noises associated with the instrumentation used to collectdata, environmental influences on the collected data, and/or noise dueto the human interaction with the instrumentation, such as movement ofthe sensor. As with the hemodynamics process model 810, the sub-modelsof the hemodynamics observation model 820 optionally share information.For instance, movement of the sensor noise is added to environmentalnoise. Optionally and preferably, the hemodynamics observation model 820shares information with and/provides information to the hemodynamicsprocess model 810.

The hemodynamics dynamic state-space model 805 receives inputs, such asone or more of:

-   -   hemodynamics state parameters 830;    -   hemodynamics model parameters 840;    -   hemodynamics process noise 850; and    -   hemodynamics observation noise 860.

Examples of hemodynamics state parameters 830, corresponding to stateparameters 730, include: radial pressure (P_(w)), aortic pressure(P_(ao)), time (t), a spectral intensity (I) or a related absorbancevalue, a reflectance or reflectance ratio, such as a red reflectance(R_(r)) or an infrared reflectance (R_(ir)), and/or a spectral intensityratio (I_(R)). Examples of hemodynamics model parameters 840,corresponding to the more generic model parameters 740, include: heartrate (HR), stroke volume (SV), and/or whole-blood oxygen saturation(SpO₂). In this example, the output of the hemodynamics dynamicstate-space model 805 is a prior probability distribution function withparameters of one or more of the input hemodynamics state parameters 830after operation on by the heart dynamics model 812, a static number,and/or a parameter not directly measured or output by the sensor data.For instance, an input data stream is optionally a pulse oximeteryielding spectral intensities, ratios of intensities, and a percentoxygen saturation. However, the output of the hemodynamics dynamicstate-space model is optionally a second physiological value, such as astroke volume of the heart, which is not measured by the inputbiomedical device.

The hemodynamics dynamic state-space model 805 optionally receivesinputs from one or more additional models, such as an irregular samplingmodel, which relates information collected at irregular or non-periodicintervals to the hemodynamics dynamic state-space model 805.

Generally, the hemodynamics dynamic state-space model 805 is an exampleof a dynamic state-space model 210, which operates in conjunction withthe probabilistic updater 220 to form an estimate of a heart stateparameter and/or a cardiovascular state parameter.

Generally, the output of the probabilistic signal processor 200optionally includes a measure of uncertainty, such as a confidenceinterval, a standard deviation, and/or a standard error. Optionally, theoutput of the probabilistic signal processor 200 includes:

-   -   a filtered or smoothed version of the parameter measured by the        medical meter; and/or    -   a probability function associated with a parameter not directly        measured by the medical meter.

Example I

An example of a pulse oximeter with probabilistic data processing isprovided as an example of the hemodynamics dynamic state-space model805. The model is suitable for processing data from a pulse oximetermodel. In this example, particular equations are used to furtherdescribe the hemodynamics dynamic state-space model 805, but theequations are illustrative and non-limiting in nature.

Heart Model

An example of the heart model 812 is used to further described anexample of the hemodynamics dynamic state-space model 805. In thisexample, cardiac output is represented by equation 1,

$\begin{matrix}{{Q_{CO}(t)} = {{\overset{\_}{Q}}_{CO}{\sum\limits_{1}^{\delta}{a_{k}{\exp \left\lbrack \frac{- \left( {t - b_{k}} \right)^{2}}{c_{k}^{2}} \right\rbrack}}}}} & (1)\end{matrix}$

where cardiac output Q_(co)(t), is expressed as a function of heart rate(HR) and stroke volume (SV) and where Q_(co)=(HR×SV)/60. The valuesa_(k), b_(k), and c_(k) are adjusted to fit data on human cardiacoutput.

Vascular Model

An example of the vascular model 814 of the hemodynamics state-spacemodel 805 is provided. The cardiac output function pumps blood into aWindkessel 3-element model of the vascular system including two statevariables: aortic pressure, P_(ao), and radial (Windkessel) pressure,P_(w), according to equations 2 and 3,

$\begin{matrix}{P_{w,{k + 1}} = {{\frac{1}{C_{w}R_{p}}\left( {{\left( {R_{p} + Z_{0}} \right)Q_{CO}} - P_{{CO},k}} \right)\delta \; t} + P_{w,k}}} & (2) \\{P_{{ao},{k + 1}} = {P_{w,{k + 1}} + {Z_{0}Q_{CO}}}} & (3)\end{matrix}$

where R_(p) and Z_(o) are the peripheral resistance and characteristicaortic impedance, respectively. The sum of these two terms is the totalperipheral resistance due to viscous (Poiseuille-like) dissipationaccording to equation 4,

Z ₀=√{square root over (ρ/AC _(l))}  (4)

where ρ is blood density and C_(l) is the compliance per unit length ofartery. The elastic component due to vessel compliance is a nonlinearfunction including thoracic aortic cross-sectional area, A: according toequation 5,

$\begin{matrix}{{A\left( P_{CO} \right)} = {A_{\max}\left\lbrack {\frac{1}{2} + {\frac{1}{\pi}{\arctan \left( \frac{P_{CO} - P_{0}}{P_{1}} \right)}}} \right\rbrack}} & (5)\end{matrix}$

where A_(max), P₀, and P₁ are fitting constants correlated with age andgender according to equations 6-8.

A _(max)=(5.62−1.5(gender))·cm²  (6)

P ₀=(76−4(gender)−0.89(age))·mmHg  (7)

P ₁(57−0.44(age))·mmHg  (8)

The time-varying Windkessel compliance, C_(w), and the aortic complianceper unit length, C_(l), are related in equation 9,

$\begin{matrix}{C_{w} = {{lC}_{l} = {{l\frac{A}{P_{\infty}}} = {l\frac{A_{\max}\text{/}\left( {\pi \; P_{1}} \right)}{1 + \left( \frac{P_{\infty} - P_{0}}{P_{1}} \right)}}}}} & (9)\end{matrix}$

where l is the aortic effective length. The peripheral resistance isdefined as the ratio of average pressure to average flow. A set-pointpressure, P_(set), and the instantaneous flow related to the peripheralresistance, R_(p), according to equation 10,

$\begin{matrix}{R_{p} = \frac{P_{set}}{\left( {{HR} \cdot {SV}} \right)\text{/}60}} & (10)\end{matrix}$

are used to provide compensation to autonomic nervous system responses.The value for P_(set) is optionally adjusted manually to obtain 120 over75 mmHg for a healthy individual at rest.

Light Scattering and Absorbance Model

The light scattering and absorbance model 816 of the hemodynamicsdynamic state-space model 805 is further described. The compliance ofblood vessels changes the interactions between light and tissues withpulse. This is accounted for using a homogenous photon diffusion theoryfor a reflectance or transmittance pulse oximeter configurationaccording to equation 11,

$\begin{matrix}{R = {\frac{I_{ac}}{I_{dc}} = {\frac{\Delta \; I}{I} = {\frac{3}{2}{\sum\limits_{s}^{1}{{K\left( {\alpha,d,r} \right)}{\sum\limits_{a}^{art}{\Delta \; V_{0}}}}}}}}} & (11)\end{matrix}$

for each wavelength. In this example, the red and infrared bands arecentered at about 660±100 nm and at about 880±100 nm. In equation 11, I(no subscript) denotes the detected intensity, R, is the reflectedlight, and the alternating current intensity, I_(ac), is the pulsatingsignal, ac intensity, or signal; and the background intensity, I_(ds),is the direct current intensity or dc intensity; a, is the attenuationcoefficient; d, is the illumination length scale or depth of photonpenetration into the skin; and r is the distance between the source anddetector.

Referring again to the vascular model 814, V_(a) is the arterial bloodvolume, which changes as the cross-sectional area of illuminated bloodvessels, ΔA_(w), according to equation 12,

ΔV _(a) ≈r·ΔA _(w)  (12)

where r is the source-detector distance.

Referring again to the light scattering and absorbance model 816, thetissue scattering coefficient, Σ_(s)′, is assumed constant but thearterial absorption coefficient, Σ_(a) ^(art), which represents theextinction coefficients, depends on blood oxygen saturation, SpO₂,according to equation 13,

$\begin{matrix}{\sum\limits_{a}^{art}{= {\frac{H}{v_{i}}\left\lbrack {{{SpO}_{2} \cdot \sigma_{0}^{100\%}} + {\left( {1 - {SpO}_{2}} \right) \cdot \sigma_{0}^{0\%}}} \right\rbrack}}} & (13)\end{matrix}$

which is the Beer-Lambert absorption coefficient, with hematocrit, H,and red blood cell volume, v_(i). The optical absorption cross-sections,proportional to the absorption coefficients, for red blood cellscontaining totally oxygenated (HbO₂) and totally deoxygenated (Hb)hemoglobin are σ_(a) ^(100%) and σ_(a) ^(0%), respectively.

The function K(α, d, r), along with the scattering coefficient, thewavelength, sensor geometry, and oxygen saturation dependencies, altersthe effective optical pathlengths, according to equation 14.

$\begin{matrix}{{K\left( {\alpha,d,r} \right)} \approx \frac{- r^{2}}{1 + {\alpha \; r}}} & (14)\end{matrix}$

The attenuation coefficient α is provided by equation 15,

α=√{square root over (3Σ_(a)(Σ_(s)+Σ_(a)))}  (15)

where Σ_(a) and Σ_(s) are whole-tissue absorption and scatteringcoefficients, respectively, which are calculated from Mie Theory.

Red, K_(r) , and infrared, K_(ir) , K values as a function of SpO₂ areoptionally represented by two linear fits, provided in equations 16 and17

K _(r) ≈−4.03·SpO₂−1.17  (16)

K _(ir) ≈0.102·SpO₂−0.753  (17)

in mm². The overbar denotes the linear fit of the original function.Referring yet again to the vascular model 814, the pulsatile behavior ofΔA_(w), which couples optical detection with the cardiovascular systemmodel, is provided by equation 18,

$\begin{matrix}{{\Delta \; A_{w}} = {\frac{A_{w,\max}}{\pi}\frac{P_{w,1}}{P_{w,1}^{2} + \left( {P_{w,{k + 1}} - P_{w,0}} \right)^{2}}\Delta \; P_{w}}} & (18)\end{matrix}$

where P_(w,0)=(⅓)P₀ and P_(w,1)=(⅓)P_(i) account for the poorercompliance of arterioles and capillaries relative to the thoracic aorta.The subscript k is a data index and the subscript k+1 or k+n refers tothe next or future data point, respectively.

Referring yet again to the light scattering and absorbance models, thirdand fourth state variables, the red and infrared reflected intensityratios, R=I_(ac)/I_(dc), are provided by equations 19 and 20.

R _(r,k+1) =cΣ _(s,r)′ K _(r) Σ_(a,r) ^(art) ΔA _(w) +R_(r,k)+ν_(r)  (19)

R _(ir,k+1) =cΣ _(s,ir)′ K _(ir) Σ_(a,ir) ^(art) ΔA _(w) +R_(ir,k)+ν_(ir)  (20)

Here, ν is a process noise, such as an added random number or areGaussian-distributed process noises intended to capture the baselinewander of the two channels, Σ_(s,r)′ and Σ_(s,ir)′ are scatteringcoefficients, and Σ_(a,r) ^(art) and Σ_(a,ir) ^(art) are absorptioncoefficients.

Sensor Dynamics and Noise Model

The sensor dynamics and noise model 822 is further described. Theconstant c subsumes all factors common to both wavelengths and istreated as a calibration constant. The observation model adds noises, n,with any probability distribution function to R_(r) and R_(ir),according to equation 21.

$\begin{matrix}{\begin{bmatrix}y_{r,k} \\y_{{ir},k}\end{bmatrix} = {\begin{bmatrix}R_{r,k} \\R_{{ir},k}\end{bmatrix} + \begin{bmatrix}n_{r,k} \\n_{{ir},k}\end{bmatrix}}} & (21)\end{matrix}$

A calibration constant, c, was used to match the variance of the realI_(ac)/I_(dc) signal with the variance of the dynamic state-space modelgenerated signal for each wavelength. After calibration, the age andgender of the patient was entered. Estimates for the means andcovariances of both state and parameter PDFs are optionally entered.

Referring now to FIG. 9, processed data from a relatively highsignal-to-noise ratio pulse oximeter data source is provided for about afifteen second stretch of data. Referring now to FIG. 9A, inputphotoplethysmographic waveforms are provided. Using the hemodynamicsdynamic state-space model 805, the input waveforms were used to extractheart rate (FIG. 9B), left-ventricular stroke volume (FIG. 9C), cardiacoutput (FIG. 9D), blood oxygen saturation (FIG. 9E), and aortic andsystemic (radial) pressure waveforms (FIG. 9F). Several notable pointsare provided. First, the pulse oximeter provided a first physical valueof a hemoglobin oxygen saturation percentage. However, the output bloodoxygen saturation percentage, FIG. 9E, was processed by theprobabilistic digital signal processor 200. Due to the use of the sensordynamics and noise model 822 and the spectrometer signal transductionnoise model, noisy data, such as due to ambulatory movement of thepatient, is removed in the smoothed and filtered output blood oxygensaturation percentage. Second, some pulse oximeters provide a heartrate. However, in this case the heart rate output was calculated usingthe physical probabilistic digital signal processor 200 in the absenceof a heart rate input data source 122. Third, each of the stroke volume,FIG. 9C, cardiac output flow rate, FIG. 9D, aortic blood pressure, FIG.9E, and radial blood pressure, FIG. 9E, are second physical parametersthat are different from the first physical parameter measured by thepulse oximeter photoplethysmographic waveforms.

Referring now to FIG. 10, a second stretch of photoplethysmographicwaveforms are provided that represent a low signal-to-noise ratio signalfrom a pulse oximeter. Low signal-to-noise photoplethysmographicwaveforms (FIG. 10A) were used to extract heart rate (FIG. 10B),left-ventricular stroke volume (FIG. 10C), blood oxygen saturation (FIG.10D), and aortic and systemic (radial) pressure waveforms (FIG. 10E)using the hemodynamics dynamic state-space model 805. In each case, theuse of the probabilistic digital signal processor 200 configured withthe optional sensor dynamics and noise model 822 and spectrometer signaltransduction model 824 overcame the noisy input stream to yield smoothand functional output data for medical use.

The various models relate measurement parameters from a source medicaldevice to a second parameter not measured by the source medical device.For example, an oxygen level is related to a heart stroke volume.

Electrocardiography

Electrocardiography is a noninvasive transthoracic interpretation of theelectrical activity of the heart over time as measured by externallypositioned skin electrodes. An electrocardiographic device produces anelectrocardiogram (ECG or EKG).

The electrocardiographic device operates by detecting and amplifying theelectrical changes on the skin that are caused when the heart muscledepolarizes, such as during each heartbeat. At rest, each heart musclecell has a charge across its outer wall or cell membrane. Reducing thecharge toward zero is called de-polarization, which activates themechanisms in the cell that cause it to contract. During each heartbeata healthy heart will has orderly progression of a wave of depolarizationthat is triggered by the cells in the sinoatrial node, spreads outthrough the atrium, passes through intrinsic conduction pathways, andthen spreads all over the ventricles. The conduction is detected asincreases and decreases in the voltage between two electrodes placed oneither side of the heart. The resulting signal is interpreted in termsof heart health, function, and/or weakness in defined locations of theheart muscles.

Examples of electrocardiograph device lead locations and abbreviationsinclude:

-   -   right arm (RA);    -   left arm (LA);    -   right leg (RL);    -   left leg (LL);    -   in fourth intercostal space to right of sternum (V₁);    -   in fourth intercostal space to left of the sternum (V₂);    -   between leads V₂ and V₄ (V₃);    -   in the fifth intercostal space in the mid clavicular line (V₄);    -   horizontally even with V₄, but in the anterior axillary line        (V₅); and    -   horizontally even with V₄ and V₅ in the midaxillary line (V₆).

Usually more than two electrodes are used and they are optionallycombined into a number of pairs. For example, electrodes placed at theleft arm, right arm, and left leg form the pairs LA+RA, LA+LL, andRA+LL. The output from each pair is known as a lead. Each lead examinesthe heart from a different angle. Different types of ECGs can bereferred to by the number of leads that are recorded, for example3-lead, 5-lead, or 12-lead ECGs.

Electrocardiograms are used to measure and diagnose abnormal rhythms ofthe heart, such as abnormal rhythms caused by damage to the conductivetissue that carries electrical signals or abnormal rhythms caused byelectrolyte imbalances. In a myocardial infarction (MI) or heart attack,the electrocardiogram is used to identify if the heart muscle has beendamaged in specific areas. Notably, traditionally an ECG cannot reliablymeasure the pumping ability of the heart, for which additional tests areused, such as ultrasound-based echocardiography or nuclear medicinetests. Along with other uses of an electrocardiograph model, theprobabilistic mathematical electrocardiograph model, described infra,shows how this limitation is overcome.

Example II

A second example of a dynamic state-space model 210 coupled with a dualor joint estimator 222 and/or a probabilistic updater 220 orprobabilistic sampler 230 in a medical or biomedical application isprovided.

Ischemia and Heart Attack

For clarity, a non-limiting example of prediction of ischemia using anelectrocardiograph dynamic state-space model is provided. A normal hearthas stationary and homogenous myocardial conducting pathways. Further, anormal heart has stable excitation thresholds resulting in consecutivebeats that retrace with good fidelity. In an ischemic heart, conductancebifurcations and irregular thresholds give rise to discontinuouselectrophysiological characteristics. These abnormalities have subtlemanifestations in the electrocardiograph morphology that persist longbefore shape of the electrocardiograph deteriorates sufficiently toreach detection by a skilled human operator. Ischemic abnormalities arecharacterized dynamically by non-stationary variability between heartbeats, which are difficult to detect, especially when masked by highfrequency noise, or similarly non-stationary artifact noise, such aselectrode lead perturbations induced by patient motion.

Detection performance is improved substantially relative to the bestpractitioners and current state-of-the-art algorithms by integrating amathematical model of the heart with accurate and rigorous handling ofprobabilities. An example of an algorithm for real time and near-optimalECG processing is the combination of a sequential Monte Carlo algorithmwith Bayes rule. Generally, an electrodynamic mathematical model of theheart with wave propagation through the body is used to provide a“ground truth” for the measured signal from the electrocardiographelectrode leads. Use of a sequential Monte Carlo algorithm predicts amultiplicity of candidate values for the signal, as well as other healthstates, at each time point, and each is used as a prior to calculate thetruth estimate based on sensor input via a Bayesian update rule. Sincethe model is electrodynamic and contains state and model parametervariables corresponding to a normal condition and an ischemic condition,such events can be discriminated by the electrocardiograph model,described infra.

Unlike simple filters and algorithms, the electrocardiograph dynamicstate-space model coupled with the probabilistic updater 220 orprobabilistic sampler 230 is operable without the use of assumptionsabout the regularity of morphological variation, spectra of noise orartifact, or the linearity of the heart electrodynamic system. Instead,the dynamic response of the normal or ischemic heart arises naturally inthe context of the model during the measurement process. The accurateand rigorous handling of probabilities of this algorithm allows thelowest possible detection limit and false positive alarm rate at anylevel of noise and/or artifact corruption.

Electrocardiograph with Probabilistic Data Processing

FIG. 11 is a schematic of an electrocardiograph dynamic state-spacemodel suitable for processing electrocardiogram data, includingcomponents required to describe the processes occurring in a subject.The combination of SPKF or SMC filtering in state, joint, or dualestimation modes is optionally used to filter electrocardiograph (ECG)data. Any physiology model adequately describing the ECG signal isoptionally used, as well as any model of noise and artifact sourcesinterfering or contaminating the signal. One non-limiting example ofsuch a model is a model using a sum of arbitrary wave functions withamplitude, center and width, respectively, for each wave (P, Q, R, S, T)in an ECG. The observation model comprises the state plus additiveGaussian noise, but more realistic pink noise or any other noiseprobability distributions is optionally used.

Still referring to FIG. 11, to facilitate description of theelectrocardiograph dynamic state-space model 1105, a non-limitingexample is provided. In this example, the electrocardiograph dynamicstate-space model 1105 is further described. The electrocardiographdynamic state-space model 1105 preferably includes a heartelectrodynamics model 1110 corresponding to the dynamic state-spacemodel 210 process model 710. Further, the electrocardiograph dynamicstate-space model 1105 preferably includes a heart electrodynamicsobservation model 1120 corresponding to the dynamic state-space model210 observation model 720. The electrocardiograph process model 1110 andelectrocardiogram observation model 1120 are further described, infra.

Still referring to FIG. 11, the electrocardiograph process model 1110optionally includes one or more of a heart electrodynamics model 1112and a wave propagation model 1114. The heart electrodynamics model 1112is a physics based model of the electrical output of the heart. The wavepropagation model 1114 is a physics based model of movement of theelectrical pulses through the lungs, fat, muscle, and skin. An exampleof a wave propagation model 1114 is a thorax wave propagation modelmodeling electrical wave movement in the chest, such as through anorgan. The various models optionally share information. For example, theelectrical pulse of the heart electrodynamics model 1112 is optionallyan input to the wave propagation model 1114, such as related to one ormore multi-lead ECG signals. Generally, the process model 710 componentsare optionally probabilistic, but are preferentially deterministic.Generally, the observation model 720 components are probabilistic.

Still referring to FIG. 11, the electrocardiogram observation model 1120optionally includes one or more of a sensor noise and interference model1122, a sensor dynamics model 1124, and/or an electrode placement model1126. Each of the sensor noise and interference model 1122 and thesensor dynamics models 1124 are optionally physics based probabilisticmodels related to noises associated with the instrumentation used tocollect data, environmental influences on the collected data, and/ornoise due to the human interaction with the instrumentation, such asmovement of the sensor. A physics based model uses at least one equationrelating forces, electric fields, pressures, or light intensity tosensor provided data. The electrode placement model 1126 relates toplacement of the electrocardiograph leads on the body, such as on thearm, leg, or chest. As with the electrocardiograph process model 1110,the sub-models of the electrocardiograph observation model 1120optionally share information. For instance, a first source of noise,such as sensor noise related to movement of the sensor, is added to asecond source of noise, such as a signal transduction noise. Optionallyand preferably, the electrocardiograph observation model 1120 sharesinformation with and/provides information to the electrocardiographprocess model 1110.

The electrocardiograph dynamic state-space model 1105 receives inputs,such as one or more of:

-   -   electrocardiograph state parameters 1130;    -   electrocardiograph model parameters 1140;    -   electrocardiograph process noise 1150; and    -   electrocardiograph observation noise 1160.

Examples of electrocardiograph state parameters 1130, corresponding tostate parameters 730, include: atrium signals (AS), ventricle signals(VS) and/or ECG lead data. Examples of electrocardiograph modelparameters 1140, corresponding to the more generic model parameters 740,include: permittivity, E, autonomic nervous system (ANS) tone orvisceral nervous system, and a heart rate variability (HRV). Heart ratevariability (HRV) is a physiological phenomenon where the time intervalbetween heart beats varies and is measured by the variation in thebeat-to-beat interval. Heart rate variability is also referred to asheart period variability, cycle length variability, and RR variability,where R is a point corresponding to the peak of the QRS complex of theelectrocardiogram wave and RR is the interval between successive Rs. Inthis example, the output of the electrocardiograph dynamic state-spacemodel 1105 is a prior probability distribution function with parametersof one or more of the input electrocardiograph state parameters 1130after operation on by the heart electrodynamics model 1112, a staticnumber, a probability function, and/or a parameter not measured oroutput by the sensor data.

An example of an electrocardiograph with probabilistic data processingis provided as an example of the electrocardiogram dynamic state-spacemodel 1105. The model is suitable for processing data from anelectrocardiograph. In this example, particular equations are used tofurther describe the electrocardiograph dynamic state-space model 1105,but the equations are illustrative and non-limiting in nature.

Heart Electrodynamics

The heart electrodynamics model 1112 of the ECG dynamic state-spacemodel 1105 is further described. The transmembrane potential wavepropagation in the heart is optionally simulated using FitzHugh-Nagumoequations. The heart model 1112 is optionally implemented, for instance,as a coarse-grained three-dimensional heart anatomical model or as acompartmental, zero-dimensional model of the heart. The latter couldtake the form, for instance, of separate atrium and ventriclecompartments.

In a first example of a heart electrodynamics model 1112, a first set ofequations for cardiac electrodynamics are provided by equations 22 and23,

$\begin{matrix}{\overset{.}{u} = {{{div}\left( {D{\nabla u}} \right)} + {{{ku}\left( {1 - u} \right)}\left( {u - a} \right)} - {uz}}} & (22) \\{\overset{.}{z} = {{- \left( { + \frac{u_{1}z}{u + u_{2}}} \right)}\left( {{{ku}\left( {u - a - 1} \right)} + z} \right)}} & (23)\end{matrix}$

where D is the conductivity, u is a normalized transmembrane potential,and z is a secondary variable for the repolarization. In thecompartmental model, u_(i) becomes either the atrium potential, u_(as),or the ventricle potential, u_(vs). The repolarization is controlled byk and e, while the stimulation threshold and the reaction phenomenon iscontrolled by the value of a. The parameters μ₁ and μ₂ are preferablyempirically fitted.

A second example of a heart electrodynamics model is presented, whichthose skilled in the art will understand is related to the first heartelectrodynamics model. The second heart electrodynamics model isexpanded to include a restitution property of cardiac tissue, whererestitution refers to a return to an original physical condition, suchas after elastic deformation of heart tissue. The second heartelectrodynamics model is particularly suited to whole heart modeling andis configured for effectiveness in computer simulations or models.

The second heart electrodynamics model includes two equations, equations24 and 25, describing fast and slow processes and is useful inadequately representing the shape of heart action potential,

$\begin{matrix}{\frac{\partial u}{\partial t} = {{\frac{\partial}{\partial x_{i}}d_{ij}\frac{\partial u}{\partial x_{j}}} - {{{ku}\left( {u - a} \right)}\left( {u - 1} \right)} - {uv}}} & (24) \\{\frac{\partial v}{\partial t} = {{ɛ\left( {u,v} \right)}\left( {{- v} - {{ku}\left( {u - a - 1} \right)}} \right)}} & (25)\end{matrix}$

where Σ(u,v)=ε₀+u₁v/(u+u₂). Herein, the approximate values of k=8,a=0.15, and ε₀=0.002 are used, but the values are optionally set for aparticular model. The parameters u₁ and u₂ are set for a given model andd_(ij) is the conductivity tensor accounting for the heart tissueanisotropy.

Further, the second heart electrodynamics model involves dimensionlessvariables, such as u, v, and t. The actual transmembrane potential, E,and time, t, are obtained using equations 26 and 27 or equivalentformulas.

e [mV]=100u−80  (26)

t [ms]=12.9t[t.u.]  (27)

In this particular case, the rest potential E_(rest) is about −80 mV andthe amplitude of the pulse is about 100 mV. Time is scaled assuming aduration of the action potential, APD, measured at the level of aboutninety percent of repolarization, APD₀=330 ms. The nonlinear functionfor the fast variable u optionally has a cubic shape.

The dependence of ε on u and v allows the tuning of the restitutioncurve to experimentally determined values using u₁ and u₂. The shape ofthe restitution curve is approximated by equation 28,

$\begin{matrix}{{APD} = \frac{CL}{\left( {{aCL} + b} \right)}} & (28)\end{matrix}$

where the duration of the action potential, APD, is related to the cyclelength, CL. In dimensionless form, equation 28 is rewritten according toequation 29,

$\begin{matrix}{\frac{1}{apd} = {1 + \frac{b}{cl}}} & (29)\end{matrix}$

where apd=APD/APD₀, and APD₀ denotes APD of a free propagating pulse.

Restitution curves with varying values of parameters u₁ and u₂ are used,however, optional values for parameters u₁ and u₂ are about u₁=0.2 andu₂=0.3. One form of a restitution curve is a plot of apd vs. cl, or anequivalent. Since a restitution plot using apd vs. cl is a curved line,a linear equivalent is typically preferred. For example, restitutioncurve is well fit by a straight line according to equation 30.

$\begin{matrix}{\frac{1}{apd} = {k_{1} + \frac{k_{2}}{cl}}} & (30)\end{matrix}$

Optional values of k₁ and k₂ are about 1.0 and 1.05, respectively, butare preferably fit to real data for a particular model. Generally, theparameter k₂ is the slope of the line and reflects the restitution atlarger values of CL.

The use of the electrodynamics equations, the restitutions, and/or therestitution curve is subsequently used to predict or measure arrhythmia.Homogeneous output is normal. Inhomogeneous output indicates abifurcation or break in the conductivity of the heart tissue, which hasan anisotropic profile, and is indicative of an arrhythmia. Hence, theslope or shape of the restitution curve is used to detect arrhythmia.

Wave Propagation

The electric wave model 1114 of the ECG dynamic state-space model 1105is further described. The propagation of the heart electrical impulsethrough lung and other tissues before reaching the sensing electrodes isoptionally calculated using Gauss' Law,

$\begin{matrix}{{\nabla{\cdot {E(t)}}} = \frac{u_{i}(t)}{ɛ_{0}}} & (31)\end{matrix}$

where μ_(i)(t) is the time-varying charge density given by the heartelectrodynamics model and ε₀ is the permittivity of free space, which isoptionally scaled to an average tissue permittivity.

Sensor Dynamics

The sensor dynamics model 1124 of the ECG dynamic state-space model 1105is further described. The ECG sensor is an electrode that is usuallyinterfaced by a conducting gel to the skin. When done correctly, thereis little impedance from the interface and the wave propagates toward avoltage readout. The overall effect of ancillary electronics on themeasurement should be small. The relationship between the wave andreadout can be written in general as:

V(t)=G(E(t))+N(p)+D(s,c)  (32)

where G is the map from the electrical field reaching the electrode andvoltage readout. This includes the effect of electronics and electroderesponse timescales, where N is the sensor noise and interference modeland D is the electrode placement model.

Sensor Noise and Interference Model

The sensor noise and interference model 1122 of the ECG dynamicstate-space model 1105 is further described. The sensor noise enters theDSSM as a stochastic term (Langevin) that is typically additive but witha PDF that is both non-Gaussian and non-stationary. Optionallynon-stationarity is modeled from the perturbation, p, representing bothexternal interference and cross-talk. One way to accomplish this is towrite:

N(E(t),p)=αn ₁ +βpn ₂  (33)

where alpha, α, and beta, β, are empirical constants and n₁ and n₂ arestochastic parameters with a given probability distribution function.

Electrode Placement Model

The electrode placement model 1126 of the ECG dynamic state-space model1105 is further described. This model is an anatomical correction termto the readout equation operating on the sagittal and coronalcoordinates, s and c, respectively. This model varies significantlybased on distance to the heart and anatomical structures between theheart and sensor. For instance, the right arm placement is vastlydifferent than the fourth intercostal.

Optionally, the output from the electrocardiograph probabilistic modelis an updated, error filtered, or smoothed version of the original inputdata. For example, the probabilistic processor uses a physical modelwhere the output of the model processes low signal-to-noise ratio eventsto yield any of: an arrhythmia detection, arrhythmia monitoring, anearly arrhythmia warning, an ischemia warning, and/or a heart attackprediction.

Optionally, the model compares shape of the ECG with a reference look-uptable, uses an intelligent system, and/or uses an expert system toestimate, predict, or produce one or more of: an arrhythmia detection,an ischemia warning, and/or a heart attack warning.

Referring now to FIG. 12A and FIG. 12B, the results of processing noisynon-stationary ECG signals are shown. Heart rate oscillationsrepresentative of normal respiratory sinus arrhythmia are present in theECG. The processor accomplishes accurate, simultaneous estimation of thetrue ECG signal and a heart rate that follows closely the true values.Referring now to FIGS. 13A and FIG. 13B, the performance of theprocessor using a noise and artifact-corrupted signal is shown. A cleanECG signal representing one heart beat was contaminated with additivenoise and an artifact in the form of a plateau at R and S peaks(beginning at time=10 sec). Estimates by the processor remain close tothe true signal despite the noise and artifact.

Fusion Model

Optionally, inputs from multiple data sources, such as sensors ormedical instruments, are fused and used in the probabilistic digitalsignal processor 200. The fused data often include partially overlappinginformation, which is shared between models, used in a fused model,and/or is used in a global model to enhance parameter estimation. Theoverlapping information results in benefits of the fused model,including:

-   -   enhanced accuracy of an estimated parameter;    -   enhanced precision of an estimated parameter;    -   noise artifact reduction in a data stream; and/or    -   an additionally determined metric.

Herein, fusion of data from biomedical sensors is used to illustrate thebenefits of sensors fusion in combination with a physical model.However, the concept extends to cover mechanical systems using sensors.

Data Fusion

Referring now to FIG. 14, an overview of a sensor fusion system 1400 incombination with at least one physical model and a probabilisticprocessor 200 is provided. Generally, data from multiple instruments1405 is provided to the probabilistic processor 200, such as to theprobabilistic updater 220, dual or joint estimator 222, state parameterupdater 224, and/or the model parameter updater 226. More particularly,data from a first instrument 1410, second instrument 1420, thirdinstrument 1430, and/or n^(th) instrument 1440 is provided to theprobabilistic processor 200, where n is a positive integer, such as atleast 2, 3, 4, or 5. One or more of the n instruments 1405 optionallyinclude readings from multiple sensors. As a first example, if the firstinstrument 1410 is a pulse oximeter, then output from the pulse oximeteras input to the probabilistic processor 200 optionally includes one ormore of: raw sensor data, voltage data, processed spectral intensitydata, or pulse oximeter generated output data, such as a blood oxygensaturation percentage. As a second example, if the second instrument1420 is an electrocardiograph device, then output from theelectrocardiograph device as input to the probabilistic processor 200optionally includes one or more of: raw sensor data, current, voltage,resistance, processed electrocardiograph device signal, and/or anoutcome, such as an indication of a previous heart attack. In a thirdexample, output from an instrument includes environmental information,such as temperature, pressure, vibration, and humidity. Herein, timereadings are optionally input along with any of the sensor data from anyof the multiple instruments 1405, but time is not considered a sensedvalue nor does time count as one of the multiple data sources fused withthe probabilistic processor 200. The fused sensor data 1450 refers toany form, matrix, concatenation, combination, union, representation, ormathematical combination of the data from the multiple instruments 1405.The fused sensor data 1450 is preferably fused by use of theprobabilistic processor 200 but is optionally fused prior to input intothe probabilistic processor 200.

Referring now to FIG. 15, an example of a pulse oximeter 1510 and anelectrocardiograph meter or device 1520 used as inputs to theprobabilistic processor 200 is provided. The pulse oximeter 1510provides time dependent values to the probabilistic processor 200, suchas raw sensor data, voltage data, processed spectral intensity data, orpulse oximeter generated output data, such as a blood oxygen saturationpercentage. The electrocardiograph meter 1520 additionally provides timedependent values to the probabilistic processor 200, such as raw sensordata, current, voltage, resistance, processed electrocardiograph devicesignal, and/or an outcome, such as a previous heart attack indication.The pulse oximeter 1510 data and electrocardiograph device 1520 data areoptionally fused, as described supra. As discussed, infra, additionalinput data is provided to the probabilistic processor 200, such as datafrom an accelerometer 1530, data from a time meter 1550, and/or datafrom an environment meter 1540, such as temperature, pressure,vibration, humidity, and/or position information. The data is at leastpartially fused into fused sensor data 1450, as described supra.

Integration of Fused Data with Probabilistic Processor

Referring now to FIG. 16, an example of data originating from themultiple instruments 1405 as input to the dual or joint estimator 222 isprovided. As illustrated, the data from the multiple instruments 1405,described supra, is optionally input into the state parameter updater224 or into the model parameter updater 226. As described, supra, thedata from the multiple instruments 1405 is optionally fused prior toand/or after entry into any of the probabilistic processor 200sub-components or software algorithms. Similarly, the initialprobability distribution function parameters 310 optionally includeinitial values/probabilities for each of the multiple instruments 1405.

Fusion Configured Dynamic State-Space Model

Referring now to FIG. 17, an example of a dynamic state-space model 210configured for use with data from the multiple instruments 1405 isprovided.

Process Model

For example, the process model 710 of the dynamic state-space model 210,optionally includes a first process model 712 related to data from thefirst instrument 1410 and a second process model 714 configured to useand represent data from the second instrument 1420. Generally, there areabout n process models 716 related to the n instruments 1440, though 1,2, 3, or more process models are optionally configured to represent orprocess the data from the n instruments.

Observation Model

Similarly, the observation model 720 of the dynamic state-space model210, optionally includes a first observation model 722 related to datafrom the first instrument 1410 and a second observation model 724configured to use and represent data from the second instrument 1420.Generally, there are about n observation models 716 related to the ninstruments 1440, though 1, 2, 3, or more observation models areoptionally configured to represent or process the data from the ninstruments.

State and Model Parameters

The dynamic state-space model optionally receives state parameter 730inputs. Examples of DSSM inputs include:

-   -   a first state parameter 732, such as a parameter from the first        instrument 1410;    -   a second state parameter 734, such as a value measured by the        second instrument 1420; and    -   an n^(th) state parameter 736, such as a parameter determined by        the dynamic state-space model 210.

Similarly, the dynamic state-space model 210 optionally receives modelparameter 740 inputs. Examples of model parameter inputs include:

-   -   a first model parameter 742, such as a parameter from the first        instrument 1410;    -   a second model parameter 744, such as a modeled value; and    -   an n^(th) state parameter 746, such as a parameter determined by        the dynamic state-space model 210.

The dynamic state-space model 210 optionally receives fusion processnoise 750 input and/or fusion observation noise 760 input.

Pulse Oximeter/Electrocardiograph Fusion

The non-limiting example of fusion of information from a pulse oximeterand an electrocardiogram device is further described to clarify modelfusion and/or information combination.

A pulse oximeter and an electrocardiograph meter both provideinformation on the heart. Hence, the pulse oximeter and theelectrocardiograph meter provide overlapping information, which isoptionally shared, such as between the hemodynamics dynamic state-spacemodel 805 and the electrocardiogram dynamic state-space model 1105.Similarly, a fused model incorporating aspects of both the hemodynamicsdynamic state-space model 805 and the electrocardiogram dynamicstate-space model 1105 is created, which is an example of a fused model.Particularly, in an electrocardiogram the left-ventricular stroke volumeis related to the power spent during systolic contraction, which is, inturn, related to the electrical impulse delivered to that region of theheart. Indeed, the R-wave amplitude is optionally correlated tocontractility. It is readily seen that other features of theelectrocardiogram also have relationships with the cardiac outputfunction. As described, supra, the pulse oximeter also providesinformation on contractility, such as heart rate, stroke volume, cardiacoutput flow rate, and/or blood oxygen saturation information. Sinceinformation in common is present, the system is over determined, whichallows outlier analysis and/or calculation of a heart state or parameterwith increased accuracy and/or precision.

Example I

Referring now to FIG. 18, a particular example of a fused dynamicstate-space model 1805 is presented. In this example, output from atraditional pulse oximeter 1510 is fused with output from a traditionalelectrocardiogram device 1520. In this example, the fused dynamicstate-space model 1805 incorporates models covering both hemodynamicsand heart electrodynamics. Generally, a fused dynamic state-space model1805 incorporates one or more models modeling information from themultiple instruments 1405.

In this example, a fused process model 1810, of the fused dynamicstate-space model 1805, includes one or more of a pulse oximeterphysiology process model 1812, the hemodynamics process model 810, anelectrocardiograph physiology model 1814, and/or the heartelectrodynamics model 1110. For instance, the pulse oximeter physiologyprocess model 1812 optionally incorporates one or more of thehemodynamics heart model 812, the hemodynamics vascular model 814,and/or the light scattering and/or absorbance model 816. Similarly, theelectrocardiogram physiology process model 1814 optionally incorporatesone or more of the heart electrodynamics model 1112 and/or the wavepropagation model 1114.

In this example, a fused observation model 1820, of the fused dynamicstate-space model 1805, includes one or more of a pulse oximeterobservation noise model 1822, the hemodynamics observation model 820, anelectrocardiograph noise model 1824, and/or the electrodynamicsobservation model 1120. For instance, the pulse oximeter observationnoise model 1822 optionally incorporates one or more of the sensordynamics and noise model 822 and the spectrometer signal transductionnoise model 824. Similarly, the electrocardiograph observation noisemodel 1824 optionally incorporates one or more of the sensor noise andinterference model 1122, the sensor dynamics model 1124, and/or theelectrode placement model 1126. Any of the process model 1810sub-models, such as the pulse oximeter physiology model 1812 andelectrocardiogram physiology model 1814 share information or data withany of: another process model 1810 sub-model, the process model 1810,the observation model 1820, or any observation model 1820 sub-model,such as the pulse oximeter model 1822 and/or the electrocardiogram noisemodel 1824.

Generally, in a fused dynamic state-space model, the process model andobservation model are optionally combined into a single model or areseparate and share information. Further, any sub-model of the processmodel or sub-model of the observation model shares information or datawith any other sub-model of the process model or observation model.

As described, supra, for the dynamic state-space model 210, the fuseddynamic state-space model 1805 for the heart optionally receives inputs,including one or more of:

-   -   pulse oximeter and electrocardiograph device state parameters        1830;    -   pulse oximeter and electrocardiograph device model parameters        1840;    -   pulse oximeter and electrocardiograph device process noise        values 1850; and    -   pulse oximeter and electrocardiograph device observation noise        values 1860.

For example, the pulse oximeter and electrocardiograph device stateparameters 1830 optionally include one or more of:

-   -   pulse oximeter related values of:        -   a radial pressure (P_(w));        -   an aortic pressure (P_(ao));        -   time (t);        -   a spectral intensity (I) or a related absorbance value;        -   a reflectance or reflectance ratio, such as a red            reflectance (R_(r)) or an infrared reflectance (R_(ir));            and/or        -   a spectral intensity ratio (I_(R)); and    -   electrocardiograph device related values of:        -   an atrium signal (AS); and/or        -   a ventricle signal (VS).

Example II

In another example, the electrocardiograph device observation parameters1840 optionally include one or more of:

-   -   pulse oximeter related values of:        -   a heart rate (HR);        -   a stroke volume (SV); and/or        -   a whole-blood oxygen saturation (SpO₂); and    -   electrocardiograph device related values of:        -   a permittivity, (ε);        -   an autonomic nervous system (ANS) tone; and/or        -   a heart rate variability (HRV).

Fusion Benefits

Several non-limiting examples of the benefits of sensor fusion using atleast one physiological model and a probabilistic processor 200 areprovided.

Stroke Volume and Contractility

In a first case, fused, fusion, or fusing of sensor data from multipleinstruments in combination with physical models of body systems yieldsadditional information not present from any given instrument of themultiple instruments 1405. Without loss of generality, an example ofgenerating a measure of stroke volume, a contractility, and/or a heartfilling rate using data from a pulse oximeter and an electrocardiographmeter is used to demonstrate the indirect parameter estimation.

Herein, benefits of combining hemodynamic information withelectrodynamic information in a fusion model is described. As described,supra, a pulse oximeter plethysmograph in combination with ahemodynamics physical model is used to determine a physical parameternot traditionally achieved from the pulse oximeter, such as a heartbeatstroke volume. Similarly, as described, supra, an electrocardiogram incombination with an electrodynamics physical model is used to determinea physical parameter not traditionally achieved from theelectrocardiograph meter, such as contractility. Stroke volume andcontractility are related, such as according to equation 34,

SV≈FR·C  (34)

where SV is stroke volume, FR, is the heart filing rate, and C iscontractility. Here, the filling rate is determined using informationindirectly measured by two systems (SV from the pulse oximeter and Cfrom the ECG). Further, given a known or approximated filling rate, theelectrocardiogram determined contractility gives information on thepulse oximeter determined stroke volume, and vise-versa.

In another case, fusing sensor data results in increased information forparameters determined with individual sensor data when the sensed dataoverlaps in terms of physiology and/or models thereof. For example, asstroke volume is an element of the heart model 812, which is tied toadditional hemodynamic models in the hemodynamics dynamic state-spacemodel, such as the vascular model 814, and the stroke volume is relatedto electrocardiograph data, as described supra, then theelectrocardiograph signal optionally aids in determination of parametersdirectly or indirectly measured by the pulse oximeter and vise-versa.Generally, the electrodynamic signal is related to the hemodynamicsignal through the use of one or more models, such as the hemodynamicsdynamic state-space model 805, the electrocardiograph dynamicstate-space model 1105, or a heart model combining two or more elementsof the hemodynamics DSSM model 805 and the electrocardiograph DSSM model1105.

Arrhythmia

As described, supra, in some systems, such as the heart, hemodynamicinformation and electrodynamic information are related. As described,supra, the hemodynamic information of stroke volume is related to theelectrodynamic information of contractility. Hence, the hemodynamicinformation of the pulse oximeter yields additional information to anyof the parameters measured by the electrocardiogram, such as anarrhythmia. Logically, if the heart is experiencing an arrhythmia, whichis being detected by the electrocardiogram probabilistic model, then theheart is experiencing diminished stroke volume, as detected by the pulseoximeter. Hence, the hemodynamic information originating with the pulseoximeter provides supporting or combinatorial information to theelectrocardiograph probabilistic model.

Similarly, a blood pressure meter yields information on blood pressure,which is related to heart function. Hence, blood pressure meterinformation is synergistic with electrocardiograph information andvise-versa. Further, blood pressure meter information is synergisticwith hemodynamic, photoplethysmograph, and/or pulse oximeter informationand vise-versa

Motion Artifact

In yet another example, patient movement results in a motion artifact inthe sensed data of a given sensor. In many of the observation models 720of the dynamic state-space model 210, a model is used that relates tosensor movement and/or movement of the body. As a first example, thehemodynamics dynamic state-space model 805 optionally uses thehemodynamics sensor dynamics and noise model 822. As a second example,the electrocardiogram dynamic state-space model 1105 optionally uses thesensor dynamic model 1124. Each of these models relate to movement ofthe sensor relative to the sensed element, such as the body. Hence, ifthe body moves, twitches, and/or experiences a bump in transport, suchas in transport by an ambulance, the body movement may be detected as amotion artifact with a plurality of sensors. For example, the pulseoximeter and the electrocardiograph device may each detect the samemotion artifact. Hence, fusion of the sensed data from multipleinstruments allows the identification of an outlier signal or motionartifact signal in data from a first sensor through detection of thesame motion artifact with a second sensor. Therefore, identification ofa motion artifact with a first sensor is used to remove the same motionartifact from data from a second sensor. Optionally, an accelerometer isused to detect motion artifacts. The fusion of input sensor data fromthe accelerometer with data streams from one, two, or more additionaldevices allows removal of the motion artifact data from the one, two, ormore additional devices.

Heart Rate Variability

In another example, sensor fusion is used to enhance a measure of heartrate variability. Generally, use of multiple sensors yields: (1) anover-determined system for outlier analysis and/or (2) varying sensortypes where not all of the sensors are affected by a noise source.Herein, heart rate variability or variation in beat-to-beat interval ofa heart is used to demonstrate each of these cases.

Heart rate variability is measured using a blood pressure meter, aphotoplethysmograph derived from a pulse oximeter, or anelectrocardiogram device. However, each of the blood pressure meter,pulse oximeter, and electrocardiogram device are subject to noise and/orpatient motion artifacts, which result in false positive heartbeatsand/or missed heartbeats.

Using a combination of sensors, such as the blood pressure meter, pulseoximeter, and/or electrocardiogram device, results in an over-determinedsystem. The over-determined system allows for outlier analysis. Byfusing the signals, an ambiguous signal from the first device isdetected and overcome by use of the signal from the second measuringdevice.

Further, noise sources affecting a first measuring device, such as apulse oximeter, are often separate from noise sources affecting a secondmeasuring device, such as an electrocardiogram meter. For instance,electrical interference may affect an electrodynamic signal, such as theelectrocardiograph, while not impacting a hemodynamic signal, such as aphotoplethysmograph. By fusing the signals, noise is recognized in onesensor data stream at a given time as the noise source is not present inthe second sensor data stream at the same time due to the noise sourcetype not affecting both sensor types.

Environment Meter

In still yet another case, sensor output from one, two, or moreinstruments is additionally fused with output from an environmentalmeter. Herein, an environment meter senses one or more of: temperature,pressure, vibration, humidity, and/or position information, such as froma global positioning system. The environment meter information is usedfor outlier determination, error correction, calibration, and/or qualitycontrol or assurance.

Generally, fusion of signals or sensor data from a plurality of devicesallows:

-   -   detection of a false positive or false negative signal from a        first device with a second device;    -   noise recognized in data from a first sensor type as the noise        is not present in a second sensor type;    -   fusion of environmental data with medical data;    -   determination of an additional parameter not measured or        independently measured with individual data types of the fused        data;    -   electrocardiograph data to aid in analysis of        photoplethysmograph data and vise-versa; and/or    -   electrodynamic information to aid in analysis of hemodynamic        information and vise-versa.

Hardware

The above description describes an apparatus for generation of aphysiological estimate of a physiological process of an individual frominput data, where the apparatus includes a biomedical monitoring devicehaving a data processor configured to run a dual estimation algorithm,where the biomedical monitoring device is configured to produce theinput data and where the input data includes at least one of: aphotoplethysmogram and an electrocardiogram. The dual estimationalgorithm is configured to use a dynamic state-space model to operate onthe input data using both an iterative state estimator and an iterativemodel parameter estimator in generation of the physiological estimate,where the dynamic state-space model is configured to mathematicallyrepresent probabilities of physiological processes that generate thephysiological estimate and mathematically represent probabilities ofphysical processes that affect collection of the input data. Generally,the algorithm is implemented using a data processor, such as in acomputer, operable in or in conjunction with a biomedical monitoringdevice. The method and apparatus are optionally implemented in a racksystem in a hospital intensive care unit, such as in connection,combination, and/or alongside other biomedical devices monitoring apatient and connected to a database system, alert station, monitoringstation, recording system, nurse station, or a doctor interface.

More generally, the probabilistic digital signal processor is a physicalprocessor, is integrated into a processor, such as in a computer, and/oris integrated into an analyzer. The analyzer is a physical device usedto process data, such as sensor data 122. Optionally, the analyzerincludes an input device, a power supply, a central processing unit, amemory storage unit, an output display screen, a communication port,and/or a wireless connector, such as Bluetooth. Preferably, the analyzeris integrated with a sensor, such as integrated into any of:

-   -   a pulse oximeter;    -   an electrocardiogram device;    -   a biomedical device;    -   a medical rack system;    -   a mechanical sensing system;    -   a complex machine;    -   a car;    -   a plane;    -   a fluid monitoring system; and/or    -   an oil transport line.

Optionally, the analyzer is configured to receive information from oneor more sensors or instruments. Generally, the analyzer is configuredfor signal processing, filtering data, monitoring a parameter,generating a metric, estimating a parameter value, determining aparameter value, quality control, and/or quality assurance.

In another example, a cardiac stroke volume analyzer comprises a systemprocessor, where the system processor comprises: (1) a probabilisticprocessor and (2) a dynamic state-space model. The cardiac stroke volumeanalyzer receives discrete first cardiovascular input data, related to afirst sub-system of the biomedical system, from a first blood pressureinstrument, such as a pulse oximeter, an electrocardiogram instrument,or a blood pressure analyzer, such as a blood pressure meter with adigital output operating on command, periodically, and/or in asemi-automated mode. The cardiac stroke volume analyzer receivesdiscrete second cardiovascular input data, related to a secondsub-system of the biomedical system, from a second electrocardiograminstrument, such as a pulse oximeter, an electrocardiogram instrument,or a blood pressure analyzer. Optionally, the cardiac stroke volumeanalyzer is an analyzer that, with or without stroke volume analysis,determines contractility or heart filling rate. Optionally andpreferably, a system processor, of said cardiac stroke volume analyzer,fuses the first input data and the second input data into fused data,where the system processor comprises: (1) the probabilistic processorconverting the fused data into at least two probability distributionfunctions and (2) at least one probabilistic model, of the dynamicstate-space model, operating on the at least two probabilitydistribution functions. Optionally and preferably, the system processoriteratively circulates at least two probability distribution functionsin the dynamic state-space model in synchronization with receipt of atleast one of: (1) updated first input data and (2) updated second inputdata. Generally, the system processor processes the probabilitydistribution functions to generate an output related to the state of thebiomedical system, such as a left ventricle stroke volume of a heart ofa patient, a measure of contractility, and/or a measure of filling rate.

Additional Embodiments

In yet another embodiment, the method, system, and/or apparatus using aprobabilistic model to extract physiological information from abiomedical sensor, described supra, optionally uses a sensor providingtime-dependent signals. More particularly, pulse ox and ECG exampleswere provided, supra, to describe the use of the probabilistic modelapproach. However, the probabilistic model approach is more widelyapplicable.

The above description describes an apparatus for generation of aphysiological estimate of a physiological process of an individual frominput data, where the apparatus includes a biomedical monitoring devicehaving a data processor configured to run a dual estimation algorithm,where the biomedical monitoring device is configured to produce theinput data, and where the input data comprises at least one of: aphotoplethysmogram and an electrocardiogram. The dual estimationalgorithm is configured to use a dynamic state-space model to operate onthe input data using both an iterative state estimator and an iterativemodel parameter estimator in generation of the physiological estimate,where the dynamic state-space model is configured to mathematicallyrepresent probabilities of physiological processes that generate thephysiological estimate and mathematically represent probabilities ofphysical processes that affect collection of the input data. Generally,the algorithm is implemented using a data processor, such as in acomputer, operable in or in conjunction with a biomedical monitoringdevice.

In yet another embodiment, the method, system, and/or apparatus using aprobabilistic model to extract physiological information from abiomedical sensor, described supra, optionally uses a sensor providingtime-dependent signals. More particularly, pulse ox and ECG exampleswere provided, infra, to describe the use of the probabilistic modelapproach. However, the probabilistic model approach is more widelyapplicable.

Some examples of physiological sensors used for input into the systemwith a corresponding physiological model include:

-   -   an ECG having about two to twelve leads yielding an ECG waveform        used to determine an RR-interval and/or various morphological        features related to arrhythmias;    -   pulse photoplethysmography yielding a PPG waveform for        determination of hemoglobins and/or total hemoglobin;    -   a multi-frequency PPG including multiple wavelengths to measure        a variety of gas concentration;    -   capnography or IR absorption yielding a real time waveform for        carbon dioxide determination, end-tidal CO₂, an inspired        minimum, and/or respiration rate;    -   a temperature sensor for continuous determination of core body        temperature and/or skin temperature;    -   an anesthetic gas sensor including nitrous oxide, N₂O, and        carbon dioxide, CO₂, used to determine minimum alveolar        concentration of an inhaled anesthetic;    -   a heart catheter yielding a thermodilution curve for        determination of a cardiac index and/or a blood temperature;    -   an impedance cardiography sensor yielding a thoracic electrical        bioimpedance reading for determination of thoracic fluid        content, accelerated cardiac index, stroke volume, cardiac        output, and/or systemic vascular resistance;    -   a mixed venous oxygen saturation catheter for determination of        SvO₂;    -   an electroencephalogram (EEG) yielding an EEG waveform and        characteristics thereof, such as spectral edge frequency, mean        dominant frequency, peak power frequency, compressed spectral        array analysis, color pattern display, and/or        delta-theta-alpha-beta band powers, any of which are used for        analysis of cardiac functions described herein;    -   electromyography (EMG) yielding an EMG waveform including        frequency measures, event detection, and/or amplitude of        contraction;    -   auscultation yielding sound pressure waveforms;    -   transcutaneous blood gas sensors for determination of carbon        dioxide, CO₂, and oxygen, O₂;    -   a pressure cuff yielding a pressure waveform for determination        of systolic pressure, diastolic pressure, mean arterial        pressure, heart rate, and/or hemodynamics;    -   spirometry combining capnography and flow waveforms for        information on respiratory rate, tidal volume, minute volume,        positive end-expiratory pressure, peak inspiratory pressure,        dynamic compliance, and/or airway resistance;    -   fetal and/or maternal sensors, such as ECG and sound        (auscultatory) sensors for determination of fetal movement,        heart rate, uterine activity, and/or maternal ECG;    -   laser Doppler flowmetry yielding a velocity waveform for        capillary blood flow rate;    -   an ultrasound and/or Doppler ultrasound yielding a waveform,        such as a two-dimensional or three-dimensional image, for        imaging and/or analysis of occlusion of blood vessel walls,        blood flow velocity profile, and/or other body site dependent        measures;    -   a perspirometer yielding a continuous or semi-continuous surface        impedance for information on skin perspiration levels; and/or    -   a digital medical history database to calibrate the model or to        screen the database for patient diseases and/or conditions.

Some examples of non-physiological sensors used for input into thesystem with a corresponding physiological model include:

-   -   an accelerometer;    -   a three axes accelerometer;    -   a gyroscope;    -   a compass;    -   light or a light reading;    -   a global positioning system, for air pressure data, ambient        light, humidity, and/or temperature;    -   a microphone; and/or    -   an ambient temperature sensor.

While specific dynamic state-space models and input and outputparameters are provided for the purpose of describing the presentmethod, the present invention is not limited to examples of the dynamicstate-space models, sensors, biological monitoring devices, inputs,and/or outputs provided herein.

Diagnosis/Prognosis

Referring now to FIG. 19, the output of the probabilistic digital signalprocessor 200 optionally is used to diagnose 1910 a system element orcomponent. The diagnosis 1910 is optionally used in a process ofprognosis 1920 and/or in control 1930 of the system.

The inventor/applicant notes that the method and apparatus fordetermination of a left ventricle stroke volume is deemed to bestatutory subject matter under 35 U.S.C. §101 as the method andapparatus, as claimed, is not a known technique and is certainly not:(1) routinely practiced in the art, (2) well-understood, (3) routine,(4) conventional, or (5) a basic building block of human knowledge.Further, the method and apparatus are not an implementation of a longstanding, fundamental, and well-known practice. Particularly, thecombination of additional elements, of: (1) a dynamic state-space model,(2) fusing sensor data, (3) a probabilistic updater, (4) iterativeupdating, and (5) the actual outcome of a measure not achievable by theindividual medical device data, viewed in combination, amount tosignificantly more than the exception by meaningfully limiting thejudicial exception.

Still yet another embodiment includes any combination and/or permutationof any of the elements described herein.

The particular implementations shown and described are illustrative ofthe invention and its best mode and are not intended to otherwise limitthe scope of the present invention in any way. Indeed, for the sake ofbrevity, conventional manufacturing, connection, preparation, and otherfunctional aspects of the system may not be described in detail.Furthermore, the connecting lines shown in the various figures areintended to represent exemplary functional relationships and/or physicalcouplings between the various elements. Many alternative or additionalfunctional relationships or physical connections may be present in apractical system.

In the foregoing description, the invention has been described withreference to specific exemplary embodiments; however, it will beappreciated that various modifications and changes may be made withoutdeparting from the scope of the present invention as set forth herein.The description and figures are to be regarded in an illustrativemanner, rather than a restrictive one and all such modifications areintended to be included within the scope of the present invention.Accordingly, the scope of the invention should be determined by thegeneric embodiments described herein and their legal equivalents ratherthan by merely the specific examples described above. For example, thesteps recited in any method or process embodiment may be executed in anyorder and are not limited to the explicit order presented in thespecific examples. Additionally, the components and/or elements recitedin any apparatus embodiment may be assembled or otherwise operationallyconfigured in a variety of permutations to produce substantially thesame result as the present invention and are accordingly not limited tothe specific configuration recited in the specific examples.

Benefits, other advantages and solutions to problems have been describedabove with regard to particular embodiments; however, any benefit,advantage, solution to problems or any element that may cause anyparticular benefit, advantage or solution to occur or to become morepronounced are not to be construed as critical, required or essentialfeatures or components.

As used herein, the terms “comprises”, “comprising”, or any variationthereof, are intended to reference a non-exclusive inclusion, such thata process, method, article, composition or apparatus that comprises alist of elements does not include only those elements recited, but mayalso include other elements not expressly listed or inherent to suchprocess, method, article, composition or apparatus. Other combinationsand/or modifications of the above-described structures, arrangements,applications, proportions, elements, materials or components used in thepractice of the present invention, in addition to those not specificallyrecited, may be varied or otherwise particularly adapted to specificenvironments, manufacturing specifications, design parameters or otheroperating requirements without departing from the general principles ofthe same.

Although the invention has been described herein with reference tocertain preferred embodiments, one skilled in the art will readilyappreciate that other applications may be substituted for those setforth herein without departing from the spirit and scope of the presentinvention. Accordingly, the invention should only be limited by theClaims included below.

1. A method for estimation of state of a biomedical system, comprisingthe steps of: providing a cardiac stroke volume analyzer, said cardiacstroke volume analyzer comprising a system processor, said systemprocessor comprising: a probabilistic processor; and a dynamicstate-space model; said cardiac stroke volume analyzer receivingdiscrete first cardiovascular input data, related to a first sub-systemof the biomedical system, from a first blood pressure instrument; saidcardiac stroke volume analyzer receiving discrete second cardiovascularinput data, related to a second sub-system of the biomedical system,from a second electrocardiogram instrument; a system processor, of saidcardiac stroke volume analyzer, fusing the first input data and thesecond input data into fused data, said system processor comprising:said probabilistic processor converting the fused data into at least twoprobability distribution functions; and at least one probabilisticmodel, of said dynamic state-space model, operating on said at least twoprobability distribution functions, said system processor iterativelycirculating at least two probability distribution functions in saiddynamic state-space model in synchronization with receipt of at leastone of: updated first input data; and updated second input data, saidsystem processor processing the probability distribution functions togenerate an output related to the state of the biomedical system, saidoutput comprising a left ventricle stroke volume of a heart of apatient.
 2. The method of claim 1, wherein said output comprises anoutput probability distribution function, wherein said outputprobability distribution function comprises both: (1) an output from aheart model of said dynamic state-space model and (2) an input to avascular model of said dynamic state-space model.
 3. The method of claim1, further comprising the steps of said dynamic state-space model:modeling physical aspects of the first sub-system using a first processmodel; modeling physical aspects of the second sub-system using aprobabilistic process model; and modeling at least one data noise sourcerelated to the fused data using an observation model.
 4. The method ofclaim 3, further comprising the steps of: said dynamic state-space modelusing a fused process model to model aspects of both the firstsub-system and the second sub-system; and said dynamic state-space modelusing a probabilistic observation model to detect motion relatedartifacts of at least one sensor used to generate the first input data.5. The method of claim 1, wherein said cardiac stroke volume analyzercomprises any of: a mechanical analyzer; and a physical medicalanalyzer.
 6. The method of claim 1, further comprising the steps of:providing a probabilistic physiological model, comprising a first heartmodel and a second vascular model; and said probabilistic model,comprising said probabilistic physiological model, sharing informationfrom the first heart model with the second vascular model.
 7. The methodof claim 1, said probabilistic model further comprising: a first modelof a hemodynamic system of a body; and a second model of anelectrodynamic system of a body that generates an electrical signal inthe absence of a sample probe.
 8. The method of claim 1, furthercomprising the step of: said cardiac stroke volume analyzer receivingdiscrete cardiovascular data from a third instrument comprising at leastone of: a Doppler system; and an ultrasound device.
 9. The method ofclaim 1, further comprising the step of: said cardiac stroke volumeanalyzer receiving discrete cardiovascular data from a third instrumentcomprising at least one of: a carbon dioxide meter; a heart catheter; animpedance cardiography device; and a pressure cuff yielding a pressurewaveform.
 10. The method of claim 1, further comprising the step of:said cardiac stroke volume analyzer receiving discrete third input data,related to a local environment outside of the cardiac stroke volumeanalyzer, from a third instrument, wherein said fused data incorporatesthe third input data.
 11. The method of claim 10, wherein the thirdinput data comprises at least one of: pressure; and humidity.
 12. Themethod of claim 1, further comprising the steps of: said cardiac strokevolume analyzer receiving accelerometer data; and said probabilisticprocessor using the accelerometer data for outlier determination in thefused data.
 13. The method of claim 1, further comprising the step of:said cardiac stroke volume analyzer generating a measure of a bloodfilling rate of a heart.
 14. The method of claim 13, further comprisingthe step of: said cardiac stroke volume analyzer generating a measure ofa contractility.